I am student with a valid F1 (student visa) status in the US. I am from Saudi Arabia. Do I need to apply for a tourist visa to go for a vacation in the Dominican Republic?
According to http://www.domrep.org/visa.html, which as far as I can tell is an official DR embassy website:
Any person who can legally travel or reside in the United States, Canada and the European Union (including Great Britain) does not need a visa to visit the Dominican Republic for tourist purposes and can enter the Dominican Republic with a Tourist Card and a valid passport.
So it would appear that thanks to your US visa status, you do not need a visa; you just need a tourist card. You can order it online or get it at the airport when you arrive. It costs US$10 and is valid for 30 days.
(If you didn't have a US visa, then as a Saudi citizen you would be required to get a tourist visa for the DR.)