In British English . . . we do not say, 'Don't you put sugar?' Unless the sentence is much longer - for example, 'Don't you put sugar in the cake mix?' But in the context of this short sentence, we say 'Don't you take sugar?' or 'You don't take sugar?' Or 'Don't you have sugar?', or 'You don't have sugar?' Even though in this example, the PT verb 'to put' is used, in British English, the equivalent in this conext is 'to take'.
this is no good. in english, "put" is used in this sense with an object and a prepositional phrase. you don't just put sugar, you put sugar somewhere or in something or on something, "i put sugar in my coffee." a sailor can be put to sea, a baby can be put to bed, the dishes can be put away, but you don't say "yes, i put sugar" that is incomplete and doesn't mean anything.