In this paper, we present an efficient algorithm for model reduction of discrete-time index-2 descriptor systems arising in context of linear time invariant (LTI) control and stability of descriptor systems. We propose a balanced truncation based model order reduction (MOR) strategy which consists of two stages. In the first stage, we reformulate the descriptor system into a generalized system by manipulating its system structure. Once the reformulated generalized system is obtained, it is applicable for a balanced truncation-based model order reduction strategy. The second stage of our work focuses is on a MOR method where the descriptor system does not require to be transformed into the generalized system. Rather, the balanced truncation MOR method can directly be applied on the index-2 descriptor system. We also implement a Smith based iterative method to compute the solutions of the Lyapunov equations corresponding to the transformed system without having to compute the projection matrices. Results from various numerical simulations are included to verify the high performance and accuracy of our proposed algorithm.