Octopuses are cephalopods, which have separate anal and oral openings. Indeed, descriptions of the cephalopod GI tract clearly depict an anal opening.
However, I am very confused about how this applies to the octopus. I don't think I've ever seen the anus depicted - where is it? What does it look like? Does anything much come out?
My first instinct would be to simply do a google image search for this. Unfortunately, those results are flooded with unrelated hits (apparently the octopus is a popular motif for tattoos... in a certain part of the body).