Photos, so we can figure out what it is?

Consider them collateral damage.

Call a tree service to cut it short and then grind the stump. Since it’s probably no thicker than your arm (I’m guessing, from your description), the cost should be fairly modest. And if you make preservation of the roses and vines adjacent, then they can take that into consideration – or you can likely collect damages from them if they don’t. In any case, they can take the risk that you prefer to avoid.

Picture. It’s pretty wilty because I cut it down a few hours ago and threw it on the trailer. It’s a hundred degrees here. It’s an ugly old thang.

@CWOTUS It’s not quite that thick. More like, if I cram three fingers together, it’s about that thick.

Um…what does a stump grinder do? If I bust my butt, can I approximate the same thing for $0?

Hm. I’m not sure what that is, but it looks more weed than tree.

I’d probably try to dig up the roots with a post-hole digger, so as to disturb the surrounding plants as little as possible, and hope it doesn’t spread.

Good idea.

Actually….Rick has a gas powered auger. I bet that would do the trick. However, he’d have to do it. Sucker is heavy and hard to control. But yeah. Just auger the shit out of it!

Actually, @Seek, a weed is any plant you don’t want in your yard. It could be an oak tree, even.
But my first thought is “weed” too…but it sure looks like it would grow into a tree if I didn’t do something.

Drill a hole ¾ of an inch in stump about three inches deep, put about an inch and a half of dilute Round-up in hole that will do it.

Roses and honeysuckle are very resilient. I would wait till just before first frost and gently dig up as much of the rose roots near this offending plant push aside and then dig and expose the roots of this offending weed and extract all that you possibly can. The rose should regroup around this disturbance and most honeysuckle are self seeding and if in doubt grab and store some of the seeds before the big dig and sow them after and next season all should be good.

I agree with @Tropical_Willie‘s solution.

Alternately, now that the tree is short again, you could paint the remaining part with Round-Up using a paintbrush. Depends on what Round-Up product if and how much you dilute.
I have a steep cliff behind my house and there were hedge trees that would send hedge balls into the yard every fall. When cut off, they just sprouted more and got uglier and more vigorous. I’d coat the sprouts with RU, and put paper towels on the stumps that I wet with RU and cover in plastic wrap and a rubber band. It took some doing, but I prevailed!
If you can kill a hedge tree, you can kill anything green.

Good ideas, guys. I thought about drilling a hole, pouring salt in and wetting it.

I tried girdling a small tree last year without reading that link or asking your question, and all I got was a grove of sucker trees.

It’s another alternative to @Tropical_Willie‘s hole drilling. I didn’t know to add the herbicide.
If your tree is small (and it is) you can girdle it with a butcher knife or hatchet. Then paint on the herbicide.

We have weed killer on hand, but it’s not RU. Will that work?

@ibstubro I read your link. “If you’d treated the chainsaw cuts you made…with an appropriate herbicide…that sucker would be dead as a hammer.”

Dead as a hammer. That made me laugh! I shall remember it!

I’m pretty sure that the photo shows more than a single year’s growth of the plant. So-called “weed trees” grow quickly (which is why we call them weed trees in the first place), but not THAT quickly. The problem is that you’re giving it some number of years to regenerate after each cutting. If all you do is cut it flush with the ground surface every year it WILL eventually die. It has to. It can only store a certain reserve of energy in the roots to regenerate after cuttings (or burnings). Eventually it has to grow leaves and start photosynthesis again to generate new energy reserves. By not cutting it EVERY year you’ve allowed it to do that. Cut every year – at least once per year, though more often would be even better – and be patient. That will kill it.

No, I cut it every year @CWOTUS. It’s weird how it just grows back as though it weren’t cut. Every year the stem, or almost trunk now, is thicker than the year before.

It looks like some sort of Mulberry to me, but, who knows.
If you saw it off at ground level and put round up on the stump end that might do it.
Make a cone around the stump from cardboard and soak the stump end with RU.

Mulberry actually sounds about right @Coloma, now that you mention it.

My view of the picture is blocked.
Round-Up is non-reactive once it reaches the soil. If your tree resembles a small bush, I’d open both ends of an appropriately sized plastic bag (clear would be good). Pull it down over the tree and tie the bottom end closed tightly around the trunk with string, bread closures, zip ties – whatever. Spray the bush/tree with brush killer or the like, and tie the top closed.
Probably the fastest way to kill it, roots and all, as you’ll be encouraging it to grow while you keep the poison undiluted. Once the bush is dead, you should be able to remove the bag in/around rain without harming the desirable plants.

I actually have some rose bushes I need to kill in the front yard and this it good brainstorming for me.

I think they have specific grass killer, @ibstubro

I want to murder rose bushes.

I don’t blame you!

About 10–12 years ago I bought rosebushes for the front yard because the S/O wanted rosebushes. Myself, I don’t believe in cultivating thorns unless they taste really good, i.e. raspberries.
Anyway, Big Lots had rosebushes, for $2. I bought red, yellow, pink, white and peace bushes.I think ultimately 2 died, and 2 lost their grafts. So I have this unsightly mess that shoots branches 4–5 foot in the air that’s covered with small, loosely leaved red “roses”.
Moral of the story: buy landscaping plants in season from a reputable plant dealer. Better yet, get starts from a local garden club.
Every year, I threaten to Round-um up, but I haven’t. Yet. This could be the year. I really need to plant a tree in that spot.