Once you unlocked an achievement and it's scanned into TSA, you can't remove the game from your TSA profile anymore.
As for the filtering in Easy Achievements (
HaxAras' Achievements), you can set the check for 'Exclude done with/no longer have' and then that game will not show achievements anymore in that overview.
Regarding the edit: There are two places for 'your games'. The Games page, and the Games Collection. From the first, you can add/remove games as you please. This will not remove any stats about them though. From your Game Collection, you are not able to remove any games where you have unlocked at least one achievement.