I don't think losing weight would necessarily put you at risk for over training, as long as it was small (2-4 pounds a week, which I wouldn't really call a 'cut').
How much weight loss a week do you think would put you at risk for overtraining?
Sorry for my late response, my first response was if you were actually cutting for a fight or something. It was is very easy to get feelings similar to overtraining when you are cutting and still training. Did you wrestle in school or anything like that? Practices right before a tournament, for me and my teams at least, they were always much harder due to be hungry as hell and thirsty as hell and sore as hell. As G-Land has been (rightly so) preaching, you get to learn yourself and your limit and for me at least, that was when it became easy.
I dont know how much weight loss a week would lead to over training, in just about all things fitness related most things are very individualized, so you should find out what feels best/works best for you to reach your goals.
I heartily accept the motto, "That government is best which governs least"; and I should like to see it acted up to more rapidly and systematically.