You may be trying to put too much arm into the throw and not enough wrist. Try practicing throwing with as minimal back swing as possible and use your wrist, then increase back swing to go where you're comfortable. You want a bent elbow and keep that elbow close to your body so your forearm and wrist does the work. Snapping the wrist is where you get both spin and speed. Step into the throw, not run. Follow through like you would throwing a ball. The main "lever" in this throw is the forearm. The secondary "lever" is the hand because it doesn't move too much relative to the forearm. The fulcrum is the elbow although it moves throught the throw. The secondary fulcrum is the wrist because it doesn't move too much relative to the elbow.
Think about "pushing" the disc rather than throwing like a ball. With a ball your shoulder is a fulcrum too. Not too much in forehand disc throw. Try to keep the plane of the disc on line to your release point as long as possible for cleaner faster releases. This is a common problem. Again practice slowly with the disc flat and "push" it, then increasing backswing (reach) and "push" it faster.