I am by no means an expert on this area--but to throw in my two cents...
I think it can be difficult, but as long as you are committed, you can make it happen. I know of several doctors (who work at religiously-affiliated hospitals) who go yearly to foreign countries to serve the poor; they have funding for such trips. [I actually know some volunteers who went on a medical mission trips to Peru and Haiti through Mercy Hospital in Baltimore; they had amazing experiences.] Opportunities do exist, but you have to search them out. If they don't exist, you can try to search out funding to start your own trips.
Also, there are a lot of opportunities locally for serving the poor (Medical Outreach Vans, free clinics). It's not as 'glamorous' as traveling to a foreign country, but there is a need. If you are not able to go yearly on foreign missions, it would be a good way to supplement your outreach to underserved populations in "off years."