I wouldn't worry about cutting one strand. Two or more strands cut, then I'd definitely say change it. Most strings, factory strings anyway, are overbuilt with more strands than they need. There shouldn't be a safety issue.

The only real potential problem I can see is maybe the string's length will not stabilize, which will cause you constant headaches with having to retune and/or reset your peep rotation every time you shoot. If that happens, then you know the string is pulling apart and you need to get rid of it.