Dumb and mute are two different words that actually seem similar in meaning, but there are few differences between them, especially in their usage in sentences. It is to be noted that it might sound impolite and inappropriate to use the word dumb in various contexts, but mute would most likely do. Dumb is an adjective that can be used to refer to the act of being speechless or lack of ability to talk base on its original meaning.
It can be used to refer to a non-living or inanimate object. Dumb, connoting its meaning is used in a device term "dumb waiter." This is a device that operates mechanically by delivering food, meals, or other items to rooms in a building. This name is given to it because, though it performs the work of a waiter, it cannot alter any speech; thus "dumb waiter." In the usage of dumb in modern English, it is used to refer to a temporal moment of being mute, probably due to shyness, fear, or shock. Mute can be used as an adjective or verb to refer to the inability to speak also.