Outside of not receiving no extra recruiting money and AP, the only other short term negative is that sometimes players will quit the team after you cut someone.
Now before you get worked up or worried about losing your star player, I haven't seen that in quite a few real life years, not even sure if that is still possible or not. But it used to be possible. When i I decide to cut someone this is not even something I factor in.
Any other negatives you will need to consider based on your returning team. I cut someone I recruited this last recruiting cycle in Phelan because the guy wasn't UNC quality even tho I recruited him, plus I had set myself up to fill his scholarship even without the extra AP and funds.