Hearthstone performs poorly on a 4k monitor with (default) 150% Windows 10 DPI scaling. Both card and board animations will stutter, the cursor will flicker, and inputs are sometimes not recognized. This was on full-screen at native 4k resolution with graphics on high (but the issue still appeared in other modes)
Adding Hearthstone as an exception to Windows System DPI scaling appears to have worked, although it results in a very small cursor.
There was a very old thread on this topic in tech support, so it seems like this issue has been around for some time