Yes you can. The newer small green cards, if written that you are a permanent resident. Those issued to families (non EU) of EU members have a validity of ten years and should be renewed automatically. These newer cards which you cannot laminate, are very badly thought out and with the minimum rubbing in your wallet, the ink will start to fade. You can take the illegible card with your passport, copies, pay the tax and renew.
Update 12/07/2015. The resident certificates or the smaller card issued to those who are not permanent residents (not legally lived in Spain for five years) Please take care of these and preferably keep in a safe place and carry a ‘copy compulsado’ Some offices for foreigners, are refusing to provide a duplicate if lost or damaged insisting that you apply for residency again.