Answer: If the yew branches are truly dead then trimming them off is fine. Neighboring branches should be able to grow into the open space and fill in the hedge.
Cutting the vines at the base will give you the opportunity to watch them this year. If they were an annual weed, you will need to be alert to seedlings coming up this spring. If the vines are a perennial plant, then you will need to be vigilant as well. Depending on what it is, you may be able to dig it out or you may need to resort to an herbicide to control it. You might want to take a sample to your county extension for help in identifying it and suggestions for how best to control it without damaging the hedge.
It is important to keep the vine from smothering or blocking light from the hedge and to keep it from constricting the trunks or branches.
Finally, although fertilizing can possibly be helpful in keeping the yews vigorous (read and follow the label instructions), the fertilizer could also potentially help the vine to thrive. Your county extension should also be able to help you monitor the yews' overall health and evaluate their need for fertilizer or other soil amendments.
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