1. Look into "System Preferences → Keyboard keys" and make sure Command is enabled and mapped to the Cmd key. Check also custom shortcuts in the "Keyboard Shortcuts" panel.

    ![Keyboard preference panel of OS X][1]

2. Go to Finder, select a file, open the "File" menu and see what shortcut is associated to "Move to Trash".

    !["File" menu of Finder][2]




  [1]: https://i.sstatic.net/pJt4V.png
  [2]: https://i.sstatic.net/Yj9NM.png