Gag Grouper Season opens June 1 in the Gulf of Mexico. Combined Red Snapper and Gag Grouper fishing trips available starting June 17th! Cinnsational Saltwater Fishing Captain Chris Mitchell ON DESTIN HARBOR 214 Harbor Blvd East pass Marina. primarily bottom fishing targeting snappers, grouper and triggerfish. Minimum of 5 hours. that's up to 4 people. 100$ for additional persons (2 max). that's offshore fishing. see land all day. 4% credit card usage fee and live bait not included.