Larimer County Colorado
Yes, thank you for the photos, and sadly that does appear to be bindweed. Unfortunately, there is no easy or magic solution. You have to be persistent and keep after it until the root is exhausted. Whether you pick it or poison it, the key is never letting it push enough new foliage to reinvigorate its root. It appears that it is growing in among your other plants. If that is true, then you probably don't want to spray it with herbicide. If it is where you can spray (or paint on with a sponge brush) an herbicide without damaging other plants, then you could use a three-way mixture containing dicamba or dichlorprop (combined with the standards 2, 4-D and MCPP/MCPA), which can provide moderate to good control.
The herbicide quinclorac is highly effective at controlling bindweed. Quinclorac is also a component of a few professional products. Quinclorac is available to the homeowner in the products Ortho Weed B Gon MAX plus Crabgrass Control and Bayer Advanced ™ All-In-One Lawn Weed and Crabgrass Killer. Remember that these herbicides are labeled only for use in lawns and can’t be legally or safely used in landscape beds or vegetable gardens.You can cut it, if there are only a few tendrils, keeping in mind that it is pesky and persistent, with deep roots, and it can continue to come back for years, but if you are persistent in removing the above ground parts (leaves, flowers and vine), it should theoretically reduce the ability to photosynthesize and therefore weaken its ability to send nutrients to the roots. You especially want to get rid of the flowers before they produce seed. But this requires rigor and constant monitoring of your flower or veggie garden to remove the pesky weed.
Here is a link to a Plant Talk article about Bindweed Control in Lawns: https://planttalk.colostate.edu/topics/lawns/1552-bindweed-control-lawns/
and a link to another Plant Talk article about Controlling Bindweed. https://planttalk.colostate.edu/topics/weeds-cultural-problems/2104-controlling-bindweed/
Best of luck !