Does "cut down on costs" make any sense?Yes, all these mean the same thing. "To reduce", "to cut back", and "to cut down" can all be used intransitively. The versions ending in prepositions should be used with an object:
We reduced costs. We reduced. (possible, though unusual by itself)
We cut back costs. We cut back.
We cut back on costs.
We cut down our expenses. We cut down. (possible, though unusual by itself)
We cut down on our expenses.