It seems that a/b is always replaced with the form: a * b^-1, Times[a, Power[b, -1]]. I tried Hold, Unevaluated, HoldAll and this always happens.

Thus a/b /. {Times -> Minus} leads to a - b^-1 and any_expression /. {Divide -> Minus} is always unchanged

How can I replace Divide in a/b with Minus to get a-b?