One’s arms are tree branches which are to bear fruit; see “fruit” and “pruned”
To dream of losing a limb symbolizes losing an aspect of yourself. You may feel disconnected from an integral part of your personality.
Dreams of a limb signify an extension of yourself. You are reaching for your goals, for connection/intimacy in your relationships, or support and partnership in your business. You are going out on a limb, taking chances and risks. See Gamble and Arm.