There is a similar expression using the word 'dumb'. but it is not 'dumb butler'. The expression is the 'dumb waiter'. A 'dumb waiter refers to the sort of manual or mechanical lift in restaurants, hotels and perhaps the homes of the rich to move completed dishes from the kitchen up (or down) to the dining area or servery. The online Oxford dictionary defines it is "A small lift for carrying things, especially food and crockery, between the floors of a building" It suggests a second definition as the turntable on some circular tables, used for moving different dishes to guests as they need them." I have not come across this use of the expression in this latter sense. This sharing device, most familiar in chinese restaurants is called (in British English, at least) a 'lazy Susan'.
The Merriam-Webster dictionary offer this definition of 'dumbwaiter' (note the spelling as one word): "a small elevator used for conveying food and dishes from one story of a building to another". But it also offer a prior definition: "a portable serving table or stand." That sounds a little closer to your 'dumb butler', but is still not a coat rack. But it might be close enough to stretch across a change of language and continent.
raisinghellyer must surely be right, however, to draw upon the synomymous word ‘valet’, and suggest that the Turkish expression (‘aptal valet’) corresponds with the dumb valet. The turkish is referring to a different substitute for a butler (or valet): not only did the butler supervise the serving of dinner in great houses: he also received and put away the coats and other impedimenta) for the householders and their guests as they arrived, and took them out and handed them back as they left. So 'dumb valet' it is. As for the different word 'valet'. In the online English/Turkish dictionary I consulted I found for 'valet' the words 'kahya' (which seems to range from general factotum all the way up to 'chamberlain') , 'kilerci' (linked to 'storekeeper', 'butler', 'cellarer', 'pantryman', 'stockman') and bas usak (defined as plain 'butler', and the word that is given first as the word for 'butler'). Frustratingly, the Turkish for 'dumb valet' turns out to be 'aptal valet', where 'aptal' means 'stupid'. This is a perfect instance of the misuse of dictionaries. 'Dumb' has as its main meaning 'speechless' in the sense of 'unable to speak'. It can stretch to mean lacking in human intelligence, as in the expression 'dumb animals'. But the dumb valet is dumb not in the sense that it is stupid but that , unlike Jeeves, it does not say "good evening sir, thank you" as you hand it your garment on arrival or "your stole, madam" as you leave, because it is without the power of speech.