Mondays have free times
On every Monday 430pm to 6 pm, you can visit Seville Cathedral completely free, and this includes an audio guide with full access to the Giralda tower.
You can reserve your place only by email. Make sure to book your visit up to 2 months in advance by sending an email to firstname.lastname@example.org. Your email should include date and time of visit, plus names of a maximum of 5 visitors. In the email, you have to give them names of the people who will be visiting.
Sunday morning mass is free
On Sundays, you can go into the Seville Cathedral and only attend mass for free. While the Cathedral is open for mass, you will only have access to the nave. There is no access to Giralda during mass timings, and the chapels and sacristies with art are all locked or cordoned off. The atmosphere is serious (with low lighting) and you cannot even walk around everywhere as you would during paid hours.
So on Sundays, the free visit during mass is not worth it unless you are going specifically for the mass. As a tourist on Sunday, you should come back for a paid visit in the afternoon.