If you have a Dubai Tourist visa and you wish cancel it, that is possible..
The cancellation charge us 40$ per visa.
Normal visas are valid for use within 60 days from the date of issue (GCC resident visas 30 days only)
Once the 60 days or 30 days are finished (i.e. Normal or GCC resident) the visa is automatically dropped, it is cancelled by the UAE immigration system because it was not used.
Once a visa is cancelled, you can apply again with the same passport or another passport.