We know from Ancient Roman statues that it was fashionable to have nails short, and – as it wasn’t elegant to cut one’s own – this would have been the responsibility of slaves or public barbers called tonsors.
In the countryside, women known as circitores travelled around offering this service, as an ancient precursor to mobile hairdressers. The barber’s equipment included shears, razors, small-blade knives, tweezers and a curved scoop for cleaning dirt under the nails.
It’s not clear which implement did the actual cutting, but the small knife seems to be the easiest to wield safely. As for modern nail clippers, the earliest patents date to the 1870s, so Roman techniques were in use for centuries.