Heat butter and 2 tablespoons oil in a large heavy pot over medium-low heat. Add garlic and red pepper flakes and cook, stirring often, until beginning to brown, about 2 minutes. Add tomatoes with juices, crushing tomatoes lightly with your hands. Increase heat to medium-high. Cook, stirring often, until sauce thickens, 10-15 minutes.
Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain pasta, reserving 1 1/2 cups pasta cooking liquid.
Add beans and wine to sauce. Cook, stirring often, until wine has almost evaporated, about 4 minutes. Add mussels and 1/4 cup pasta cooking liquid. Cover; cook, stir-ring occasionally, until mussels open, about 4 minutes (discard any that do not open).
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