Answer: Honeysuckle is difficult to control. You might try cutting it all back short and applying an herbicide containing glyphosate to the stems and stumps as per the manufacturer's directions. Make sure to find the correct strength and dilution rate for honeysuckle. This may take several applications combined with repeated cutting.
You can also try smothering it. Cut it back to the ground, then cover the stems with a layer of heavy cardboard or several sheets of newspaper and top that with several inches of mulch such as wood chips or shredded bark. Try not to bury or touch the stems of the hedge with the mulching materials. This method works by excluding light for a long period of time.
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