What is the average cost per square foot to gut and renovate a kitchen?

A lot of this will depend on materials selected to be installed and any "surprises" located once everything is ripped out...trust me, there will be some. An average kitchen, stripped to the studs and sub-floor should budget out between $15 and $20K if you are hiring sub-contractors (unless you are proficient, DO THIS!) You can cut the cost in half if you are able to competently (be serious about your abilities as screw-ups are costly) complete the job.

Budget for the following professionals for sure: electrician, plumber, drywall crew
Secondary professionals: Flooring, Cabinet Installer, Painter