It can BUT... yes there are a few "buts".  It doesn't always cut all the way through or very well.  Felt fibers are webbed and the blades don't do a very good job at cutting through nicely.   You also need to have a VERY STICKY cutting mat!  One that you have already used quite a bit will work for paper, but you won't want to try felt with it.   The stiffer felts that you can buy will cut better, but... personally I tried cutting felt with my cricut and won't be doing it again. I LOVE using my Big Shot machine to cut felt though!  I'll be doing a lot of that!

You also will have to take your blade house out and give it a good  cleaning.  The felt fuzz gets up in there and can give you problems later on with it cutting correctly.