I introduce the notion of hypertwined split-quaternionic regularity using techniques based on hypertwined analysis, a refined version of general hypercomplex theory. In the split-quaternionic and complex split-quaternionic cases, I show that hypertwined holomorphic (regular) functions admit a decomposition in a hypertwined sum of regular functions in certain subalgebras. The hypertwined quaternionic and split-quaternionic regularity theories prove to have a direct impact on reformulations of spacetime algebra quantum theories and quantum field theories.