Depends on what variety of rhododendron. Some are more resilient and invasive than others. Probably worst is Rhododendron ponticum.
Usual method is lever and mulch. ie cut the stalk down to about 1m tall. Then use that as a lever to pull out the rest of the roots. May need to dig down around it, and cut through any thicker roots.
If you leave any of the stump, make sure you cut off any green shoots. And bash the top with a hammer, should stop it regrowing.
For bigger trunks, stem injection can work. ie drill a small hole, and fill with glyphosate. It will kill off the whole plant within a few months.