is boxing with an mma bag, good and safe to build up muscle around the joints in your arm?

Dylan Bundy thinks so.

If your going to do that make sure you learn decent technique. Learn to throw your punches by “rolling your shoulder”. Dont throw a punch where the punch “snaps” with your elbow straight. Should have a little bend (minor) in the arms when the punch lands…throw the punch through the bag and make sure you wrap your wrists/hands. The last thing a pitcher needs is to injure his wrist punching a bag because it isent wrapped. If you dont know how to wrap your wrists and hands you can find good examples online, same goes for throwing a good punch. Dont throw any big overhand punches or big looping punches. Look for examples of boxers throwing punches not MMA guys, most MMA guys have terrible technique when punching.

Thanks for the replies. Am i supposed to relax my arm immediately after contact?

Relax the arm? No. If your throwing a jab you want to bring the hand back to a defensive position as quickly as you can to protect yourself. The movement should be quick but not hearky jerky.