Upvote:2
Mangalore airport has immigration staff as it is an international airport so your luggage can be checked in for your final destination (Mangalore) provided this is just one ticket. You would get boarding pass for the Mumbai-Mangalore leg at Dubai at the time of check in.
It depends on how you purchased your ticket.
For those airports in India where there is no immigration staff (airports that have no international flights) you would have to collect your luggage at the first port of entry and then check in again for your final destination.