There are two main ways to do this.
1. Pump the water out
If you look at the design for any pet fountain, you’ll see that these are most commonly set up with a recirculating pump. If you choose to have that pump transfer the water to another container, then you can use it to empty the original basin, that’s typically going to be the easiest, although obviously it’s going to require electrical power but I assume that’s OK since pretty much any automation will. So to empty the basin you just turn on the pump.
2. Provide an actuator for a gravity drain
The other alternative is a basin with a drain that has a sliding drain cover and then you use an actuator to open the drain. Think of a bathtub and then automating the open drain lever.
This is doable, but often turns out to be more expensive than just adding a pump. However, it’s a good way to completely empty the basin, which is hard to do with a pump because the pump usually needs a small amount of water to keep it primed.
For example, here’s a typical livestock waterer.
See the drain plug on the bottom? Add an actuator underneath to move that and you can drain that way.
I believe there are some commercial versions which do have this function automated, but they tend to be designed for dairy farms and are very expensive since they have to be durable enough for cattle.
So depends on the details of the use case. What exactly are you trying to do? How big is the basin and how empty does it have to get? And how durable does it have to be?