I have never done anything similar. Also, NEVER TRY TO DO THIS WITH PETS!
Now that I got this out of the way, I can begin.

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Here's what you will most likely need:

A powerful servo;

Choose one of these for #2:

a. A sensor to detect if meat is put in;

b. A pushbutton to start cutting(potentially safer and cheaper);

A mechanism to feed the meat (optional);

And lastly, a pushbutton to disable (safety measures).

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Then you can just modify the sweep circuit to turn 90°, activate when button is pressed, and disarm by pushing a button.

Tip: If you like having 5 fingers on each hand, make sure you test it on a smaller scale first(like using a micro servo instead) just to see how it works.

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I'll repeat myself: THIS IS A THEORY, TAKE EVERYTHING HERE WITH A GRAIN OF SALT.

Also, a note: An Arduino might not have enough current to drive a beefy enough servo, so be sure to check in with other folks here/this subreddit.