You can bring the damaged National Identity Card to the Social Security Office along with your birth certificate and they'll get a replacement for you. You might have to pay Rs100 for that though (this fee is payable for loss cards but it may well apply to damaged cards as well, so it might be worth to bring the cash too just in case). Here are the offices that you can go to:
- Social Security Office, Ground floor, Renganaden Seeneevassen Building, Port Louis
- Rose Hill Social Security Office
- Plaine Magnien Social Security Office
- Vacoas Social Security Office
The information given is for citizens of Mauritius. For non-citizens, you'll have to bring a certificate of naturalisation as well.