I don't understand what the preposition "mit" usage in the example above. If I was writing the sentence, I'd simply omit it.
The verb is mitkommen, and it is spilt in two parts. Therefore mit- is not a preposition but a prefix wandering about. An alternative way to phrase this would be “Willst du zu mir mitkommen?”
mitkommen verb [ intransitive ] [ trennbar, unreg., Perfekt mit sein ] /ˈmɪtkɔmən/ andere an einen bestimmten Ort begleiten
to come (along/too)
Wir gehen Eisessen, kommst du mit?
We’re going for some ice cream. Do you want to come?
Synonym → mitgehen
That means, as is someone asks another person to join in on the way.
Leaving out mit:
“Willst du zu mir kommen?”
Would be used if the person mir is already at the destination (or not, in fact) and the person called du travels alone.
Mitkommen is more like 'escort', 'accompany' or 'come along' than just 'come' (alone, by yourself, ).
From comment by Janka:
In your example, mitkommen is used as an infinitive to the modal verb wollen. The prefix is usually not split from the infinitive, and Willst du zu mir mitkommen? is in fact as valid as your example. The prefix mit- however is special in some regards. It's also one of those few prefixes you could put on an already prefixed verb, e.g. mitansehen.
I'm not entirely convinced, that this is an example of mitkommen, so my attempt here:
If one is already at home, he could suggest:
Willst Du zu mir kommen?
The mentioned sentence is typically used, if the subject is not at home but still has to go there and suggests that the addressed person joins him.
So a more exact translation would be:
Would you join me going home?
Another scenario, where mit is applicable is, if another person was asked before and already agreed, so mit means to join that different person instead of the speaker.