Robert in Zone 6
A: If you do, you're cutting into the crown and you could risk killing that plant. The only time you want to cut strawberry leaves off is after the main harvest, where you do what's called rejuvenation. And that’s where you go in and cut the leaves off and thin the plants.
For everbearing strawberries, there's not much to do now. A strawberry patch, if properly maintained and rejuvenated, can last 10-15 years.
For the less-diligent gardeners, I recommend buying new varieties every 3-4 years and planting them in a different spot of your garden.