What sorts of jobs do RMP soldiers carry out from day to day, besides guard duties.

We don’t actually carry out ‘Guard Duties’, we work a shift rotation whilst conducting General Police Duties, just to avoid any confusion you may have.
There are many specialist roles within the RMP, upon arriving at your first unit you will be expected to conducted General Police Duties, investigating cases dealing with minor and major crimes.
There are different roles throughout your career which you can take such as;
Close Protection
SIB (Special Investigation Branch)
Weapons Intelligence specialists
Local intelligence policing
Attachments with Policing agencies
Operational Training Teams
Multi Media Evidence Team
Forensic Analysis
These are just a few of the specialist roles which you can undertake throughout your career as well as operational deployments and improving your basic soldiering skills.

I hope this helps, and if you have any further questions don't be afraid to ask.