Hi there...

the term get your tongue cut off is - glossectomy.
A hemiglossectomy is where they remove half
a partial, is less than half. (in layman's terms)

How much is removed depends very much on size and location of the tumor. A small stage one tumor say on the side may require minimal removal.
A larger tumor, same area, may require removal of the area and a graft.

The same size tumor, in the middle back area of the tongue, may require a full glossectomy.

In this case they rebuild the tongue and people are able to do well with that. There are a few people here who've had this surgery and are able to talk and eat. It really depends on a lot of things. If you have cancer of the tongue, it has the potential to be HIGHLY aggressive. For the best chance of survival you need to get to a cancer center, with a top notch ENT - ;o)

best of luck.