I wouldn't saw the stump off as it'll give you something to hold on to for a bit of leverage - Yes, I've no idea how young, strong and fit you are, but I'm nearing retirement age and I'd give it a go if I wasn't off work with a slipped disc at the moment
, but I did that cleaning the windows - not gardening - I've spent the last 12 months digging out roots in this new garden with no ill effects. I'm just designed for gardening, not housework!
Go on, give it a go and post us some pics - inspire us all with new levels of Olympian digging - we need something to cheer this week 
When you get down a couple of spades' depths you can saw any roots off, they shouldn't re-shoot from that far down.