I've killed many sycamore and ash stumps over the years.
My technique is to strip as much bark as possible from the stump
down to ground level (and below) and to drill a few deep holes
in the centre of the stump using a brace with a broad auger bit.
Every time the roots send up a sucker or some more leaves, hack
them off. The lack of bark causes the live wood to die. The holes
in the centre trap rainwater which causes the centre to rot slowly.
Even the strongest sycamores give up after a year or two of this treatment.
The best tool for removing bark that I've found is a hand adze
with a blade 50mm wide from Tiranti.