Why do the Catholics and Orthodox keep relics and bone fragments? Isn't this disrespect for the body?

In Orthodoxy, cremation after death is not permitted. It is not preferred in Catholicism. This is because of the strong respect for the integrity of the body. Both traditions are also strongly pro-life/anti-abortion. Yet all churches in these traditions must be consecrated with the relics of a saint. So is someone out there...cutting up saints' bodies?! How do these traditions understand the dignity of a body, even to the point of not destroying a dead one, but yet we disseminate these holy relics? (Please note I am not asking why we *venerate* relics, I am asking how their *creation* squares with other teachings on bodies.)