The process that is NOT carried out by the executive branch is "Fund the military."
Funding the military is primarily the responsibility of the legislative branch, specifically Congress, which controls the budget and fiscal appropriations. The executive branch can propose budgets and suggest funding levels, but the actual funding comes from legislation passed by Congress.
The other options—issuing vetoes, issuing pardons, and signing executive orders—are all processes that fall within the powers of the executive branch.