If you cut the trunk off near the bottom, and pour/brush, liberally, pure, undiluted glyphosate (41% concentrate Roundup) directly onto the freshly cut stump, the roots will draw the glyphosate down into the root system, through the cambium layer, effectively killing everything in a matter of a few days. Then after a week, you can remove the stump and not worry about suckers coming up everywhere. Do this within an hour of cutting it off.

I would think the method you propose should work. The roots you leave won’t survive long, and you should be able to keep it under control in the confined space it grows.

Brush, don’t pour the brush killer on the stump so that you don’t spill and kill nearby plants such as grass. Whether the method will work without a brush killer depends on how many roots are under the walkway and how much stored energy they have.

all you need.. is to apply it to the cambium layer ... the thin green line.. just under the bark ...

https://duckduckgo.com/?q=cambium+layer&t=ffcm&iax=images&ia=images

i use the applicator at the link to use minimal product ....

it is possible that it will sucker.. just snip those and put a drip on the snip ...

the goal is minimal product use ...

i would just cut it to the ground.. apply such.. and walk away ... dont bother digging anything up ... imo ..

return unused product to properly labeled container.. and rinse out applicator ...

ken

https://www.google.com/search?q=plochmans+mustard&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a&um=1&ie=UTF-8&hl=en&tbm=isch&source=og&sa=N&tab=wi&ei=XQTcUYCCC_OFyQGCg4DAAg&biw=1154&bih=805&sei=XwTcUbmZHZK4yAHD0oDYDw

I did some 6" to 12" Siberian Elms last year, poured a ring of Product on the freshly cut stumps and used a 2" paint brush to uniformly move it out into the edge of the inner bark/phleom layer. Also did some 1" caliper trees that were starting up around our neighbor ladys house. Works like a charm but yes, be careful with the product, it kills on contact anything green and growing.

Thank you all. I am in Canada and will not be able to get any of those products but I just cut it down and got the roots out, I will carefully watch for suckers or growth.

thanks again,