Cut the trunk as low as possible then dig, dig, dig to get all the roots - I hate ivy

thankyou that is what we are doing but for every big piece there are twenty small I hate ivy also

Ivy is acceptable to eg cover my neighbour's unsightly brick shed but I agree it's not acceptable smothering any other plant to use as a ladder to get to the light.

cut the base of the trunk as low as possible then drill a few holes in the trunk & fill them up with roundup weed killer just like killing a tree
if the trunk is very wide you may have a lot sap coming from it.