Define "sea". Is it connected to the ocean or landlocked?
Black Sea scenario:
You couldn't empty the Black Sea. Oh, if the water disappeared instantaneously, it would be briefly dry, but the ocean would surge through the Bosporus to fill it up again.
It's a wild-ass guess, but I bet it would take only a few years (ten?) to refill. Less if the Bosporus were wider. There would be catastrophic erosion along the banks and floor of the Bosporus.
There would be some temporary weather changes, such as a decrease in precipitation in the surrounding area, especially on the side that is downwind for the prevailing winds, but the weather would gradually return to normal as the water level rises (more precisely, as the surface area increases).
The ecosystem right along the shoreline would be destroyed, of course. But I'm not sure how severe the effect would be as you move farther out to areas that weren't wetlands to begin with. There would be some domino effects as changes in one ecosystem trigger changes for its neighbors.
Rivers running into it would flow much faster, possibly draining some lakes completely. There would be tremendous erosion damage along the course of those rivers.
If people were living around it, fishing probably provided a significant part of their diet, so expect a famine. That would be further aggravated by reduced precipitation for crops. In a Black Sea scenario, the crop reduction would be fairly short term, though. Fish population would take time to recover, on the other hand, so fishing wouldn't be able resume right away.
Caspian Sea scenario:
Maybe you mean something the size of the Black Sea but landlocked like the Caspian Sea? That's really just a huge, slightly salty lake. There are still rivers running into it so it would eventually fill back up, but now we're talking about a very long time: possibly centuries, more likely millennia.
You would get the same shoreline ecosystem loss mentioned above and the same torrential flow and erosion of the rivers. You also get the same weather changes, but instead of being temporary, they become essentially permanent, so are better referred to as climate changes.
Google Lake Bonneville. The main difference there is the salt. When Lake Bonneville evaporated, the salt was left behind. Presumably your magical accident would remove the salt along with the water. (Or are you boiling the water away? That would leave the salt behind, but then you need to account for the effects of that much heat.)