I think it's a matter of your definition of mixin and ultiple-inheritance. Support for mixins can be a way for an otherwise single-inheritance language to support a form of multiple-inheritance. Does that make it a multiple-inheritance language?
The specific example I'm familiar with is Ruby, which supports mixins ("modules"), but is otherwise an explicitly single-inheritance language. It uses a form of implicit ordered search path/chain to determine which method runs if there are multiple candidates.