At first I thought you had to sell items in the store and live with the regret of picking it up in the first place, but Beatskin class has a passive skill that explicitly interacts with the discard item mechanic. But how do you do it?

Oh, there it is. Right click.

I was playing on a Surface Book and for some reason the stlyus right-click wasn't registering with it. Switch to a mouse and suddenly right click does lots of things.