Yes, dough can be overworked, and the resulting biscuits will either be hard as hockey pucks, or won't rise as much.
What you do, however, isn't overworking. Overworking would be kneading it until the dough isn't as smooth or sticky, and actually turns out crumbly. Reworking the leftover dough to shape new biscuits isn't going to overwork the dough, as long as you don't continue handling it and re-knead it a lot. Just a few times, until you can roll it out again is fine.
Not a trained chef, but have taken several cooking classes, one on bread, biscuits and pastries. :)