Same problem here: Cinnamon on Linux Mint 17 (Rebecca), same Java-version. Whenever I start Minecraft in 1.8.1 and press Alt+Tab, Ctrl+Alt+[ArrowKey], try to regulate my volume via the keys or pause audio playback, Minecraft vanishes and the following stop to work: Alt+Tab, Expo & Scale (Window and virtual desktop overwiews), mouseclicks (I can still move the cursor around, its just utterly useless).
(Also, possibly related, on the first two tries with 1.8.1 the game didn't start at all.)
Game still minimizes in 1.10.2, but can be recorvered with Alt+Tab. (At least on my new machine, after all it's been over two years without anything happening on this bug.)