Familysearch.org has the civil death, birth and marriage records for many towns in Puerto Rico. Most of the records begin some time in the late 1800's. They also have some of the church records beginning in the 1600's but the selection of towns is limited and Yauco is not one of them. The trick here is that most of these records have not been indexed yet so you will have to spend some time looking at the index photos for your ancestor. If you have an idea of the years you need to look at, then it is not too cumbersome; however, if you don't, be prepared to spend a lot of time combing through the books.
The death indexes begin with 1889 but there are records beginning in 1885 with embedded handwritten indexes that are a bit harder to find. They are usually at the end of each book. Each photo set includes 4-5 books. Each book has its own index and has about 500 records.
I am also researching family in Yauco so, if you tell me the likely years, I can keep an eye out for his name when I look through the indexes.
The direct link to the Yauco records is https://familysearch.org/search/image/index#uri=https%3A%2F%...