I managed to cut down a tree by accident once. Technically I uprooted it rather than cut it down - it was about two inches tall and I caught it in some garden tools not noticing it was there.
I took a couple of conifers out of my back yard some years ago. I cut the branches off and fed them to a shredder, then tied a heavy rope between the two trunks and twisted it to break as many roots on both sides as I could. Then I used a hand trowel and dug away earth around the roots so I could cut the with a hooked saw (I tried chopping them but my axe just bounced off them).
A neighbor took the trunks away and I guess he used them for firewood.
