Is there a way to kill garden weeds & vines without using chemicals?

Get out there and dig them out or hire someone to do for you. Use boiling water or epsom salt followed by boiling water on the offending weeds. I use vinegar too, but not good around lilacs.

Japanese Honeysuckle is a common invasive plant in the Southeast. The shade tolerant vine occurs along field edges, right-of-ways, under dense canopies, and high in canopies. This invasive vine colonizes by prolific vine growth and seeds that are spread by birds.

Here are four ways to help control this invasive plant; the first three are organic and the last is chemical.

1. Mowing and/or grazing is one way that an individual can rid their property of honeysuckle. For this technique to be effective one will need to start while the vine is small. Continue with this technique until you never see starts popping up through the ground again. This can take several years and in doing you will need to be diligent in your technique.
2. Pulling up and/or cutting down is another approach one can use. The pulling aspect comes when the plant is small or little starts begin to appear. Make sure to pull the roots completely out of the ground. If the plant is too big, prune it down to the ground with hedge trimmers. You will need to use this type of equipment because the vine’s branches are very thick.
3. Smothering is a technique that can be used once the material has been removed by another approach, such as mowing or cutting down. To do this, cover the area first with cardboard and then 4 to 6 inches of mulch. Doing this will prevent the plant from being able to perform photosynthesis and in doing so it will starve. Leave the cover on for at least a year and add to the mulch layer as needed to keep the depth.
4. The last approach is to kill the honeysuckle with a brush killer but for it to be effective you must remove it from the environment first. Once that is done, you can then apply the herbicide. Unless it is a large infestation, vines in the home landscape (on fences or arbors) can be cut back to ground level in late summer and the cut ends treated with undiluted glyphosate concentrate (53.8% preferable but 41% okay).

If a thicket is present, cut all stems back to the ground with a mower or weed-eater, if possible. Allow the cut stems to re-sprout, then spot-spray the sprouts with a 5% solution of glyphosate with surfactant.

If mechanical vine control prior to herbicide application is impractical, you can spray the stand with a 5% glyphosate and surfactant solution in late summer, but note that non-target plants may be at higher risk with this method. Increase solution strength if necessary and re-treat as needed for complete control.

Note: Some sources recommend foliar-spraying on a warm day in winter to reduce damage to other non-target plants but this has not proven to be a reliable method as the honeysuckle has to be actively growing to take up the herbicide and the non-target plants have to be completely dormant.

Get out your weed killer, cut off the offending plants and paint with a strong grass and weed killer on the cut stumps only. It will eventually absorb into the roots and not harm your other plants you want to keep. You may need to repeat it, but make sure you don't get it on anything but the cut stump.

Vinegar plus salt in a spray bottle should kill most of the weeds on a sunny hot day.

Vinegar