Tips to avoid fondant from falling apart:
Dust flat dry hard surface mat with corn starch.
Roll out the fondant to 1/8 thickness or thicker. Let it sit for a few minutes.
Use the stamp or cutter on it like you would making sugar cookies.
Let it sit a little more and then take a really thin knife to work it off the mat carefully.
If you can put it to the side and let it harden a little more, it should be easier to apply to the cupcake.
Recommendation: use store bought fondant.