Look at these examples:
You should clean the milk seen as you spilt it.
You should clean the milk seeing as you spilt it.
Which one is correct, and how is it grammatically defined/termed?
Seeing as is the generally accepted form; I don't recall ever hearing anyone say seen as (though it's possible I just didn't notice).
Grammatically speaking, seeing as is a conjunction; it fills the same function here as because. The Oxford English Dictionary defines it this way:
Its history goes at least as far back as 1504: