No, not at all. 'Do' can mean many different things in many different contexts. In fact, 'mimic' or 'imitate' is quite a rare meaning of 'do'. 'Do' only means this if the context is, say, a show in which performers are doing impressions of famous people, for example. In other contexts, the verb 'do' can have dozens of other meanings. If the context is a hairdressers, for example, 'they do you' can mean that the staff cut your hair - the possibilities are endless.