The main environmental impact associated with eutrophication is hypoxia. Hypoxia is when a body of water has levels of oxygen below those necessary to support most life. The excess algae growth in the Gulf of Mexico is rapidly followed by algae die-offs that increase decomposition across the water column. This decomposition sucks all the oxygen out of the water resulting in a state of hypoxia.
Since oxygen levels are reduced across the water column, biodiversity is severely affected and die-offs may occur for multiple species. As hypoxia tends to be more severe near the bottom of a body of water, animals that live at these depths suffer the most. While mobile organisms like fish can potentially move out of hypoxic waters and into other waters nearby, organisms such as crabs and mussels cannot and are therefore some of the organisms that suffer the most as a result of hypoxia. Even mobile organisms that can move to adjacent waters can be impacted by overcrowding. As the available space of suitable habitat is reduced, more and more fish have to move into the same space causing overcrowding. This can lead to increased competition for food resulting in reduced growth and size, cannibalism, decreased survival rates for young fish, and disrupted food webs.
Hypoxia Infographic (EPA: https://www.epa.gov/ms-htf/hypoxia-101)
Fish Kill Image (National Geographic: https://www.nationalgeographic.com/news/2010/9/100916-fish-kill-louisiana-gulf-oil-spill-dead-zone-science-environment/)