This is funny because the word "croak" has two meanings.  It usually refers to the sound that we say that a frog makes.  So that's why it makes sense to say that the frog croaked after the princess kissed it.

But "croak" in slang, also means to die.  So it ends up sounding like after she kissed the frog, it died.

I guess the semicolon is important because if it were a comma, it might be what someone said.  In other words, someone might have croaked those words.  Like if you wrote "Hello," she said.