Heat olive oil in a large saucepan or dutch oven over medium heat.
Add onion and garlic and sauté until onion softens, about 2 to 3 minutes.
Add the blood orange beer to the saucepan and bring mixture to a boil. Then reduce to a simmer and add the mussels to the pot.
Cover pot and let the mussels cook until the shells open, about 4 to 6 minutes.
Add 2 Tbsp butter, blood orange zest, and lime zest to the pot and stir to combine, reserving a little bit of the orange and lime zest for garnish.
Transfer mussels with a slotted spoon to a separate bowl, discarding any mussels that didn't open. Spoon cooking liquid over the mussels.
While the mussels are cooking, bring a pot of lightly salted water to a boil. Add linguine to pot and let pasta cook until al dente.
Drain pasta and return to pot with 1 Tbsp butter and pomegranate molasses. Stir well to combine.
Serve linguine in bowls and top with mussels, some of the cooking liquid, pomegranate arils, blood orange slices, and additional zest.