Program slicing is widely used in applications such as program comprehension, software testing, debugging, measurement, and reengineering. This paper proposes a new approach for program slicing, called modular monadic slicing, basing on modular monadic semantics of the program analysed. We abstract the computation of program slicing as a language-independence entity: slice monad transformer. On the basis of this, we present and illustrate modular monadic dynamic and static slice algorithm in detail. We conclude that modular monadic slicing has excellent flexibility and reusability properties comparing with the existing program slicing algorithms. It computes program slices on abstract syntax directly without intermediate structures such as dependence graphs.