can you provide some pictures, as I am NOT sure what all your talking about
what is half OFF
is the DEER a shoulder mount, that was attached to a wooden backer, is the hide pulling off a the form UNDER the hide, and so on
all will sort of have different fixes
if your NOT sure, you can also just take the mount to a taxidermist shop and ask them HOW to fix, or HAVE them fix it for you

pending age of mount, depends on HOW and what was used to mount it, and as such, so will how and what you use to FIX it
so without GOOD pictures and better info here
we really cannot help you

a shop will be your best bet maybe , if you don;t want to do the work yourself too?
but a shop will know what to do and what this mount is made of!if you don;t know to tell us!