PokéBase - Pokémon Q&A
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This is apparently some glitch to get a second Mewtwo in game. I don't know if he's referring to the Daycare, but that can only hold one Pokémon at a time. I doubt this is a possibility, but I wanted to check with you guys to be sure.

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This is the glitch that sumwun is talking about: https://bulbapedia.bulbagarden.net/wiki/Mew_glitch
I don't think I could provide a good walkthrough of how to get Mewtwo specifically, but that link may be useful as a general guide.
So after defeating/running away from the Ditto with the desired copied Special stat, do you just walk through tall grass for a wild Pokémon encounter? Or are more steps involved?
No. That is impossible to breed Mewtwo.
It's impossible to breed anything in Yellow, and the asker already knows this.
It's possible to get Mewtwo by performing glitches.

1 Answer

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The easiest way to manipulate the last encountered Special stat when performing the glitch is to first obtain it on one's own Pokémon, and battle a wild Ditto. Send out the Pokémon with the desired Special stat on itself, and wait for the wild Ditto to use Transform. As the move Transform copies all of the target's stats, the Ditto will take on the Special stat of the Pokémon sent out. After defeating it or running away, proceed as normal, being sure to not battle any other Pokémon before the end of the glitch. If the Ditto is captured, the result will be based off Ditto's Special instead.

The Special stat on the player's own Pokémon can be caused either by natural leveling or by stat experience.

In Pokémon Yellow, as wild Ditto can only be found in the basement of Pokémon Mansion or Cerulean Cave, it is highly recommended to bring an Escape Rope or a Pokémon who knows Dig, in order to leave the Mansion immediately after battling the Ditto. If the player attempts to walk out of the Mansion and encounters another wild Pokémon on the first floor, its Special stat will overwrite that of the Ditto and cause a different Pokémon than the one desired to be encountered.

Mewtwo's index number is 131, so you need to use a Pokemon whose special stat is 131.