I am UAE resident but Indian citizen I have already travel to Spain but that time there was a bit of a mistake in my passport which I didn't notice that time. That mistake was with my date of birth - my real date of birth is 31/03/93 but by mistake my country embassy made a mistake and wrote 21/03/93 which is now clear. But will this issue be a great issue or what should I do?
This should be fine.
If your passport has the wrong date of birth, then as far as Spain is considered, that is your official date of birth. So use the "wrong" date of birth for all associated travel documentation (visa, tickets, etc), and you will not have any problems. The passport is the only piece of ID you really need for overseas travel, so there's no chance of them seeing any other birth date for you.
The only hypothetical situation I could see this causing problems is if you're renting a car, and your driver's license has a different DOB, and the rental agency notices the difference, and is not satisfied by your explanation. That's four ifs in a row, and even if it does happen, you can just try another agency.
Also, in the future, if you renew your passport and get the date fixed, and you apply for a new visa and are asked about previously granted visas, it would be wise to attach a note saying that previous visa X was granted for passport number Y, which due to a clerical error had the wrong date of birth Z. Otherwise they may have trouble finding your old visa, and the difference in dates may raise flags if they do match it.