As a general rule for all ForeverLawn artificial turf products, mowers, weed wackers, and edgers should be kept off of your turf. It is OK to trim natural grass near your putting green, as long as care is taken to avoid direct contact between the blades or wire of the power equipment and the green.
To maintain your putting green, groom the grass with a plastic leaf rake, stiff bristled push broom, or power broom to help keep grass looking fresh. When doing this, pull the items against the lay of the turf to lift the blades. Learn more about GolfGreens maintenance here.