Yes you do need to clean your coffee grinder out at least once per month or more depending on how often you use the coffee grinder.
When you grind coffee beans the coffee beans oils and particles can cling to every nook and cranny inside the coffee grinder eventually leading to decreased performance.
It also makes your coffee taste bad or at least less fresh when you don't have a clean coffee grinder.
I use a little vinegar and water to clean out my coffee grinder at least once per week.
Just soak a rag in some vinegar and water and wipe down the inside of the coffee grinder with it.
Then run some water inside the coffee grinder and dry it out.
Just don't submerge the coffee grinder in water.
You just want to rinse the vinegar off the coffee grinders inside so that it does not make the coffee taste like vinegar.