We introduce Mosaic, a sparse tensor algebra compiler that can bind tensor (sub-)expressions to external functions of other tensor algebra libraries or compilers. Users can extend Mosaic by adding new functions and can bind a sub-computation to a function using a scheduling API. Mosaic substitutes the bound(sub-)expressions with the specified function call and automatically fills in the rest of the unbound code using a default code generator. Mosaic also has a search system that can automatically map an expression to a set of registered external functions. Both the explicit binding and automatic search are verified by Mosaic. We demonstrate the benefits of our approach by showing that calling hand-written CPU and specialized hardware functions can provide speedup of up to 206x and 173x, respectively, over a homogeneous compiler. Mosaic’s external function interface is simple and general. Currently, 38 external functions have been added to Mosaic, with each addition averaging 20 lines of C++ code.