Clue on Petey's map.

When Mark find Petey's map on the back of their team photograph- the first thing it shows says "We are here because we're not all there."

"Not all there"- in the head. They are all severed because they are mentally dealing with something that makes them "not all there" which makes someone WANT to sever their minds, so the part of there mind, that makes them "not all there" wont interfere with work- that's why the innies "are here" on the severed floor.

My theory is that these people are severed as mostly part of a psychological experiment. Which is why Petey wrote MIND at the top- it's all about how the mind works.