The reason why Republicans want to entirely defund USAID but avoid touching a hair on the defense budget is that they see every single matter of foreign affairs as a nail, and so they don't understand why we should be spending money on anything other than hammers.
Larison, not a big fan of foreign policy hammers, takes issue with labeling aid a part of defense:
Republicans didn’t vote to cut defense. To claim that they support “defense” cuts because they want to de-fund USAID is to abuse the phrase “defense spending” even more than hawks already do. The RSC supported cutting foreign aid spending because they don’t think of most foreign aid as having any importance for national security policies, and to the extent that they acknowledge that foreign aid funding is directed to Afghanistan and Pakistan they would probably point to this as one of the problems with “Af-Pak” policy.