Removing a tree stump is beating me

How big is it? That decides everything. Under about a foot across you can usually dig around it, cut the roots with a pruning saw or a reciprocating saw with a long blade, and lever it out. Bigger than that, rent a stump grinder for half a day, it's quicker than a weekend of digging. Get the utility lines marked before grinding. The drill-holes-and-stump-remover route works but takes months, not weeks.