You don't have to get a tetanus booster shot every 10 years but it's advisable anyway since it prevents you from getting an tetanus infection should you step on a rusty nail or get cut from rusty metal.
You can always get a tetanus shot after getting cut but if you've already had a tetanus shot within 10 years before you got cut then you won't need another tetanus shot as long as it's been within 10 years since your last tetanus shot.