Every time you remove rust from your hedge clippers, you are removing layers of metal. And each time this happens, your hedge clippers become less effective. The best way to care for your hedge clippers is to prevent them from developing rust in the first place. Clean your hedge clippers with soap and water after each use. Then coat them with a thin layer of motor oil before putting them away.
Remove light layers of rust by scrubbing the affected areas with steel wool.
Remove significant amounts of rust by soaking your hedge clippers in white vinegar for 10 minutes. Then scrub them with a stiff wire brush.
Remove significant amounts of rust--that have left the hedge clipper blades rough or pitted--by sanding them away with an electric drill with a wire-brush attachment. But keep in mind that while this will remove the rust, it will remove some of the hedge clippers' metal and likely reduce their effectiveness. The best option may be to replace heavily rusted hedge clippers.
Coat your hedge clipper's blades with a thin coat of motor oil after the rust is removed.