Abrasive waterjet.

Somehow I doubt that was the answer you wanted... so of the less expensive options a bandsaw is your best bet by far, but if you don't have access to one a jigsaw/scrollsaw will work. You want to use lots of coolant (though lubrication isn't an issue, you can even get away with water) and go pretty slow, in addition to using a coarse wood cutting blade.

Problem with HDPE is the same as a lot of thermoplastics, it will soften and melt very easily from cutting heat resulting in a messy cut, bound up blade, or the material reforming itself behind the blade. Those are the best ways to avoid it.