I understand that it's a pun incorporating 토끼, but I'm having trouble figuring out what it means. I've seen it used in Kakao and Instagram.
토끼고싶다 - I want to ditch this scene.
It has a negative connotation. A nicer way to say the same thing might be:
도망가고싶다 - I want to escape/run away.
It's also heard used like this as a collective (we):
토끼자 - Let's ditch this place.
And this way in the past (1st person or collective) tense:
토꼈어 - i/we ditched that place.
Again, it's kind of not nice.
It may sounds like a slang and the certainly the usage may be so. However, it is a word that is listed in the Korean dictionary.
I used "토꼈어" mostly in the situation where any authority might have a say on the issue.