Call a professional tree removal company to "grind" the stump", or dig down to the roots, cut each one as you find it and remove it whole. Hack it into chunks as you work and remove chunks.

Building a fire is slow, and you run the risk of it smoldering underground in the roots for months - I had a tenant who tried that route and he almost burned down the fence whan the fire broke out a week or so later where a root surfaced near the fence.

The chemical removers are also slow ... and don't work well in phoenix vecause it's so dry.