The directions on the label should guide you toward the most effective use of the product. But if you are still not sure, please say what product you have.

For an ongoing indefinite setup, this does not sound good. Spraying should be used as occasionally as possible as a last resort.

Depending on if it's your driveway or other non-vehicle area, you could replace the gravel with 12" patio bricks, poured concrete, mowed area, or other plan that could help you get away from spraying as a continued form of maintenance.

If and ONLY if there are no trees and other desired vegetation anywhere nearby or "downstream", the herbicide imazapyr will keep things from growing for at least a year. There are consumer formulations at the big box stores, but I would instead strongly recommend you hire a professional applicator.

However I basically agree with Tiffany you are trying to use herbicides to treat what is really a landscape design or hardscaping issue, i.e. the lack therefore.

As for your question, it's better to spray before cutting, wait until the weeds appear totally dead which can take 10-14 days with glyphosate (aka "roundup"), then cut them. It translocates through the leaves into the roots so if you cut then spray, there's less leaf tissue to absorb it.