This
link will take you to the Alaska Industry Support Alliance website. The Alliance is a trade organization formed by companies that support the oil, gas, and mining industries up here. Their jobs link doesn't actually list jobs, but it lists the job websites of all the members. Most of the North Slope jobs are not with the oil companies, but with these support companies.
I know several guys who've gotten on with Schlumberger lately; most of these contractors should be hiring, although the current slump in oil prices has people being cautious right now.
Generally, the oil and gas industry will be hiring and growing over the next several years (I don't know much about mining, sorry). A lot of current slope workers are getting ready to retire, and the industry didn't do a very good job of developing a sustained workforce. Most thought that the Slope would play out by now, so they didn't try to bring in a new generation. Now we're trying to play catch up, so it's a great opportunity to get your foot in the door.
Like the previous poster said, though, you might need to take a laborer job to get started (slick line, etc), and once you're up there and you've proven that you're reliable, doors will open for better positions in the things you are looking for.
God bless!
Greg