My GD just turned 10 and I let her cut but while I am supervising her. I first do a couple to show her and than let her try it. She does a good job at it.
I think it depends on the maturity of the child. Perhaps let him practice on small squares and such and if he is responsible to listen to rules and abide by them he may be ok.
If you feel really uncomfortable than do it for him and let him learn by watching and perhaps let him try later on.