Network share to network share copy

Today I am finding my machine bogged down copying files from one network share to another network share. It seems like such a waste to transfer bits to my CPU just to forward them on to another server. You'd think that the fileserver and the destination server could just send the packets directly to each other and send me a notification when finished.

This is probably something that is easily done by someone with network experience, but I'm stumped. And my PC is crawling.