The word “cuss” is probably a bastardization of “cursing,” which is the opposite of blessing. Both cursing and blessing involve whatever diety is considered by the curser/blesser to be most powerful. Similarly, the word “swearing” is related to making an oath, which again, was usually to the most powerful diety a person could imagine. Picure Will Ferrell saying “by Great Odin’s beard!” in Anchorman.
Anyway – I imagine Jesus replaced Mithras or Dionysus or whatever as he got more popular.