I've cut lots of players in the past and like bow2dacowz says, the impact isn't as much as keeping bad players.
This season is the first time I've ever had a player transfer on me when I cut someone else. I'd just taken over at George Fox, had 1 scholarship to fill and thought I could cut a low-ATH/DEF big to make room in case I could squeeze in 2 recruits, or at least get extra budget money next season. I was surprised when one of my better guards just jumped ship saying he couldn't trust me after I'd cut the big.
My rep is still A+ (I hadn't recruited the guy I cut), my loyalty is A- after a lateral move from Bethany.
This may have been my imagination but it just seemed to me that recruits were not dropping to me with B prestige as much as they did at Bethany with C+ prestige - 2 drops out of 100 phone calls just doesn't seem normal, but who knows. If there's something to that, I suspect it was the fact that I was a first-year coach at a new school. Shrug.