Neha,
Speech difficulties are very common following surgery and radiation to the tongue/neck. Part of this is due to the problem of trying to pronounce words normally when a significant portion of the tongue is missing, and part is due to the inflammation and dry mouth that typically result from radiation. A rule of thumb that you will read from time to time on this site is that you can expect to need a month of recovery time for every week of radiation treatment. If he only finished treatment a month ago, he's probably about at the worst stage of side effects right now, but hopefully should begin to see some improvement over the next few weeks.
Depending on the stage of cancer involved and the nature of the treatment, people recover at different rates and also regain varying levels of speech ability, so it's hard to generalize about what your father will experience. However, if he continues to have great difficulty speaking after a few months, he may want to consider going to a speech therapist.
Is your father being treated at a major cancer center? What is his schedule for followup visits with his doctors?
Cathy