There can only be one improvement per tile. Putting a manufactory on a mined tile will eliminate the mine, but you will still have the underlying tile yield. So, for example, if the mine was on a hill, the hill contributes 2 hammers and the mine contributes 1 hammer -- replacing the mine with a manufactory would, in that case, result in a tile yield of 5 hammers (2 from hill an 3 from manufactory).
For this reason it is generally advisable NOT to put manufactories on hills, since the yield from a mined hill eventually will be greater (e.g., with Chemistry). It is preferable to put manufactories (and most other great person tile improvements) on a tile that is at least food neutral (enough food to feed the citizen working the tile), such as non-riverside grasslands; even better is a 3-food tile, like cattle or grasslands wheat.