How can I tell if these leaves were eaten by sawflies?

Look closely at the plant, especially underneath leaves and along stems, for larvae. Sawfly larvae can look a lot like small caterpillars, and their feeding can leave leaves ragged or stripped. A clear photo of the insect, the damaged leaves, and the whole plant would make identification much more reliable.

If you’re seeing pale, silvery scars or tiny speckles rather than chunks missing from the leaf, thrips are another possibility. Check for tiny slender insects and little dark specks on the leaves. That kind of damage is different from the obvious chewing and defoliation you’d expect from larger larvae.

Before spraying, confirm what the plant is and what’s feeding on it. For now, you can inspect and remove visible larvae by hand if there aren’t many. Don’t assume a treatment meant for caterpillars will work on sawflies, and follow the product label if you choose a pesticide.

If the plant is boxwood, a box tree moth is one possibility, but that pest feeds on boxwood, not plants generally. On a different kind of plant, that would point you elsewhere. The plant’s identity is a useful first clue, along with a photo of the larvae.