If you tax imports and subsidize exports, the nominal exchange rate adjusts so that those policies don’t end up improving the real exchange rate at all, and thus the trade balance will not improve. In other words, you get a stronger dollar and indeed we already see that.
This can be shown with offer curves (think of international trade as a kind of barter, and think of imposing two offsetting taxes on that barter; does anyone know of an on-line demonstration of this?). Do note there are possible ambiguities due to the complexity of actual, real world forms of taxation, and furthermore real world exchange rate determination is not well understood, neither are changes in exchange rates. That said, those ambiguities could just as easily work against the mercantilist proposal as for it.
Since many of Trump’s proposals, such as import-taxing tax reform, seem to involve versions of this idea, those proposals probably will not work.