been there done that, best way is to
1. start out with a pick/shovel & trench spade to knock off as much clay dirt & rocks as you can. do this all the way around
2. toss the knocked off dirt & clay off into the bucket of the tractor & move it away dump & return until most of the easily to access dirt is off. (Keep the walking & working area clear of the majority of loose dirt as it is hard to work around & will make it better in long run.)
3. get out the ax & knock off the roots some all around the stump & repeat cleaning as you go of excess dirt prior to getting water out there.
4. power wash smaller sections where it can be cut off (large roots at the base say.) Work mostly on one side when doing this so it can be rolled easier in later steps.
5. get a 100 buck chain saw & a spare chain & go after the big exposed roots & top that you can get to hacking off all the chunks ya can. Sale prices are cheap now. look at a electric one as they can take some abuse & will have a better warranty

OR rent a DEMO (demolition saw)
6. repeat until you can roll it up on its side.
7. repeat the dirt removing process & keep going until you can move it out of the yard..Mark