I would think with some tees and valves you should be able to rig something up?
With a single dosing pump? Yes, but the pump would have to be able to run backwards (on a schedule or for a set amount of time, it would be difficult if you had to hold a 'reverse' button the entire time).
In any case, a dosing pump with, let's call it the input side, in the tank. On the 'output' side you'd have a T, and then each side of the T would have a check valve, pointing in opposite directions. The check valve allowing water to flow away from the pump, goes to the drain. The check valve allowing water to flow towards the pump goes to the new saltwater.
In normal operation, the pump will draw water from the DT, through the pump and send it to the drain while keeping the other valve closed. If you reverse the pump, it'll draw water up from the new saltwater bucket and send it to the tank while the valve on the waste side remains closed.
My gut says it would be easier to just use two pumps and eliminate all the valves. But, OTOH, this seems like a fairly elegant solution to both empty and fill the tank with a single pump. A bit of extra maintenance since those cheap valves go bad from time to time (and it may be hard to notice, depending on how things are set up) and a some extra connections where things can leak. But with that, it would also give you the ability to do everything with a single app/single pump.
Anyone have a water removal setup to go with their mixing station.
And to get back to this question, a lot of people have a 'water removal setup'. Look for "Auto water changer" and you'll find plenty of examples. Pre-built, homemade, apps/controllers that can handle it etc.