Are these beets still edible?
It's a vegetable. When you cooked it you damaged the cell walls and the juice is leaking out.

I think this picture only seems unusual because of the beets' color. If these were carrots there wouldn't be a question because, of course, the juice would be less startling.

If these beets haven't started to mold or ferment- and you'd know it from the smell- then they are fine.