Really, really, really far away...several hundred miles. Mammoth is on the Eastern side of the Sierra Nevada in Central California, and not part of the Cascades.
They're part of completely different geologic systems; the Cascades volcanoes are a result of the Gorda and Juan de Fuca plates subducting (diving under) the North American plate; Mammoth is a result of the thinning of the crust caused by extension (pulling apart) of the Great Basin.
Thanks for your great info - I was wanting to see if there was any connection to the Pacific Rim volcanos - apparently not!