What alternative can someone take instead of tetracycline for mild pimples?

Hope it's just mild: Topical benzoyl peroxide isn't a bad way to start, and tea tree oil is the one "herbal / natural" stuff that probably helps some. If you've not used topical clindamycin, it's a better idea for starters than a systemic antibiotic (tetracycline's really more for more severe acne). The oral contraceptive pill can clear a woman's complexion if she wants & can take it.

Doxycycline: Minocycline, Doxycycline are related to tetracycline and are alternatives. Also other antibiotics such as clindamycin, trimethoprim-sulfamethoxazole can be used to treat mild to moderate acne.