Otdfbt

I don't know if this is exactly what you're looking for, but the verb supersede is close.

From Cambridge Dictionary:

supersede — to replace something older, less effective, or less important or official:
Wireless broadband could supersede satellite radio one day.

From Merriam-Webster

1a : to cause to be set aside

1b : to force out of use as inferior.

to supplant TFD

1. To take the place of; to replace

As in:

"The automobile supplanted the horse and buggy."

Obsolete

It's less commonly used as a verb than an adjective (my subjective opinion), but that's exactly what it means.

https://www.merriam-webster.com/dictionary/obsolete

obsolete

 verb

ob·​so·​lete |  ˌäb-sə-ˈlēt  , ˈäb-sə-ˌlēt

obsoleted; obsoleting

Definition of obsolete (Entry 2 of 2)

transitive verb

: to make (something) old-fashioned or no longer useful : make obsolete

Deprecate is a term often used with technology: e.g. a deprecated feature or framework.

From Oxford Dictionaries:

1.1 be deprecated (chiefly of a software feature) be usable but regarded as obsolete and best avoided, typically because it has been superseded.

- ‘this feature is deprecated and will be removed in later versions’

- ‘avoid the deprecated element that causes text to flash on and off’

Interestingly, you automatically used a word in your question that you didn't even comment on—perhaps without realizing what you'd done: displace:

1 a : to remove from the usual or proper place
specifically : to expel or force to flee from home or homeland

// displaced persons
1 b : to remove from an office, status, or job
1 c obsolete : to drive out : BANISH
2 a : to move physically out of position

// a floating object displaces water
2 b : to take the place of (as in a chemical reaction) : SUPPLANT

So, in your example sentence:

The automobile displaced the horse and buggy.

Consider eclipse:

to cause an eclipse of: such as

a : OBSCURE, DARKEN

b : to reduce in importance or repute

c : SURPASS

Surpass is relevant here. In essence, the automobile overshadows its earlier form. It's not that the horse and buggy is dead. It's that it has been effectively replaced as the dominant mode of travel.

The automobile eclipsed the horse and buggy.

I think "Replaced" can be used

Cambridge dictionary

to take the place of something or put in the place of something or someone else:

We replaced our old air conditioners.

The ailing actress was replaced by her understudy.

In your example it would be

The automobile replaced the horse and buggy.

From Merriam-Webster:

antiquate, verb

an·​ti·​quate | ˈan-tə-ˌkwāt

transitive verb
: to make old or obsolete

Obviate

From the Oxford Living Dictionaries

1. 
   

   Remove (a need or difficulty) ‘the presence of roller blinds obviated the need for curtains’

   
   
   

   1.1 Avoid or prevent (something undesirable)
   ‘a parachute can be used to obviate disaster’

   
   

"The automobile obviated (removed the need for) the horse-and-buggy."

Obsolesce

transitive verb

: to make obsolescent

From Merriam-Webster

Your most readily understood answer is going to be simply made obsolete. Here is why looking for something else can lead to problems:

Attempting to capture a precise meaning in a single word without context will often lead to ambiguities. While you provide context in one example, it doesn't necessarily apply in similarly worded examples.

To illustrate this, let's start with your context:

The automobile made the horse and buggy obsolete.

I'll show some counterexamples further on that would make you question the value of these choices. But using some of the most up-voted suggestions, you can ask yourself: are these statements necessarily going to mean the same?

The automobile superseded the horse and buggy.

The automobile supplanted the horse and buggy.

The automobile deprecated the horse and buggy.

The automobile displaced the horse and buggy.

The automobile eclipsed the horse and buggy.

For each of these words, there are multiple definitions. They are not all consistent with "make obsolete":

supersede: to succeed to the position, function, office, etc., of

supplant: to take the place or move into the position of

deprecate: to express disapproval of; deplore.

displace: to move from the usual or correct location

eclipse: to surpass; outshine

In choosing "the best words", you are still left with the job of ensuring that what the listener hears is the same as what you say.

If you changed the context, do these highlighted words mean "made obsolete"?

Here are the counterexamples:

In the national park, federal law supersedes state law.

This year, imported cars are expected to supplant domestically produced vehicles.

The scientists were mocked in a move to deprecate the oil industry.

The war displaced millions of people.

When Ryun eclipsed the four minute mile, it became a realistic goal for many to strive for.

It should be obvious that none of these statements conveys the notion of made obsolete.

Words with multiple meanings have their place, and they only convey their intended meaning with the right context. None of the examples above about the automobile will necessarily be understood to mean "made obsolete" except to the person who already knows that simple fact.

Alternatively, supplanted should work as well

What word means to make something obsolete?

I would use the verb 'outdate'. Although the adjective 'outdated' is more famous than the verb counterpart, the verb is in use on both sides of the pond.

According to this Oxford Dictionary:

Make out of date or obsolete.

‘new technology is outdating current privacy laws’

According to Webster-Merriam:

: to make out of date : make obsolete

the development of new machinery has outdated many plants

Make redundant, perhaps.

Redundant - superfluous, excessive; surplus; unnecessary (OED).

Outmoded?

As in: "Pagers are every rarely used these days".

overrode

The automobile overrode the horse and buggy.

Quite literally and figuratively (but it's less vivid than smashed, I think).

override (past tense: overrode; Collins English Dictionary):

1. to set aside or disregard with superior authority or power




2. to supersede or annul




3. to dominate or vanquish by or as if by trampling down

Origin of override (Online Etymology Dictionary)

I would stay with your root, expanded to 'obsolescence', and use other verbs to set it up such as:

The automobile 'ushered in', or 'drove', or 'bulldozed in', or 'steamrolled in', or 'forced', or 'engineered' the obsolescence of the horse and buggy.

Since we're talking automobiles, I like 'drove'. :)

Extinguish

For an edgy substitute, where "killed" is too strong, you might consider something along the lines of extinguished.

Extinguish means to put an end to or bring to an end; wipe out of existence; annihilate. It is derived from the same Latin as the word extinct, and in your example with the horse and buggy, the automobile is the thing that brought (or drove, if you are pun-friendly) the horse and buggy to near extinction.

So the phrase

The automobile extinguished the horse and buggy business.

is strong and empathic about the effect the auto had on the horse and buggy.

(Note: consistent with Stack Exchange guidelines, I wish to keep this answer separate from my previous answer, as it is entirely distinct from that answer, and should stand on its own.)

The automobile renders the horse and buggy obsolete is a clear and complete sentence. Why does one need to make a verb out of an adjective?

Consider deprecate, that is, according to Dictionary.com, to "depreciate, belittle". It is commonly used in technical circles, particularly software and electrical/electronics engineers, to refer to material which, while still technically working, has been replaced in full by a better technique or device and is now generally irresponsible to depend upon.

This is a fairly recent meaning for the word, though; as in the past, it generally meant to disapprove of something strongly (in a broader sense, also see Dictionary.com and Webster), or in older cases, to declare something to be evil and pray against it (Webster).

supplanted, succeeded, undermined, unseated, usurped, ejected, ousted

Automobile caused the elimination of the horse and buggy?