A stability analysis of linear discrete-time neutral systems with both discrete and distributed delays is examined. To address this problem with accuracy, Lyapunov–Krasovskii candidates (LKCs) are formulated by heterogeneously splitting the whole delay interval into various parts; then, each part is assigned functionals with different weighting matrices. Then, new stability criteria are established and expressed in the form of linear matrix inequalities (LMIs) by combining a delay decomposition approach with an auxiliary function-based summation inequality method. These criteria provide a computationally efficient framework. Finally, several numerical examples are presented to confirm the validity and expanded feasibility region of our results when compared to existing approaches.