best plan would be to dig around it, not too close to the trunk itself as there will more roots to deal with and it will make the job harder. So dig around the stump further out to expose the side roots , get a sharp axe on them , work you're way around the stump and you'll find it will loosen up very quickly, there will most likely be a central root aswell that need chopping before the root will just pull out. Not a massive task as it's not really a massive root. A morning's work with ease.
Lol, digging and cutting roots could take all day. I’m a gardener and depending on what sort of tree it was could be a mate as some roots go straight down. hire a stump grinder and should take no more than a hour and no heavy work other than using the machine which will grind it ground level.
looks to be a shrubby plant more than a tree , probably with an old climber mixed in with the stems. A close up pics does indicate a lot of old decayed wood etc , cant see it taking more than a mornings work with a decent axe and spade.
If that's one of those shrubs with the yellow coloured wood (can't remember name) then it will be an utter pig I had one that the OH wanted removed and it took one sharp and heavy axe coupled with a course blade on a rip saw, best part of several hours if I remember as the roots go everywhere and lots of closely packed branches coming up! Oh and some long armed croppers came in handy too..
