Slice of life generally revolve around the main characters dealing with the problems of every day life in their own way. Working towards adult hood and being on their own. The lack of parents in these shows are to show the characters independance and cooperation with each other, rather than their reliance on their parents to do everything for them. The ones with parents like that generally have a spoiled/stuck up back ground if you notice in these anime, compared to the ones who live their own lives in a setting and appreciate everything given to them as it comes.
In short: They want the characters to solve and work out their problems with others their own age, instead of having the "level head" of a parent to guide them to the easy answer, coasting through life.
So for the majority, they cut the parents out entirely, never meeting them or introducing them(for other characters) or have the main characters parents killed off before the series started/having them in a distant/distracted state in which they would be of no help either way.
There are some exceptions to this, but that's the general idea behind Slice of Life.
Quote from a site explaining them
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Slice of Life series don't usually have much of a plot or, if taken to extreme, even the omnipresent Conflict, but they don't really need one, and many Slice of Life stories use a lack of conflict to serve peaceful escapism rather than realism. An example of this would be how in many slice of life school stories, parents are nearly non-existent.
Quote (i_r_slayer @ 16 Sep 2013 12:43)
You could also go with this, as they really would not help the plot of it in any way. With someone giving all the answers from their own experiences, rather than the characters learning from their own experiences, we'd get bored of the show and move on to a different one that is more interesting.