A hiring freeze doesn't prevent them from replacing the current personnel, does it?
It depends on how they worked it. During Clinton they (Gore ran it) did one where it was a hiring freeze, but they did a workaround where they replaced them with contractors. It ended up costing taxpayers more money.
From what I have read, the current freeze is a freeze by attrition, so when someone quits or retires, the FTE slot is still there, but remains vacant. If vacant, the office still gets the $$$ for it and can use them for other costs (if their HQ lets them - sometimes the HQ eliminates the position and takes the money to use themselves). It can remain vacant for years, or depending on the administration and individual budgets, can be removed at a later time. Once removed, it's generally quite difficult for an office or division to get it back.
For Trump to make this freeze a money saver as well as a gov reducer, the language would need to state that the position is eliminated when the current person leaves. Otherwise agencies have less staff, but more money to blow on other stuff.