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The sensor-cloud system (SCS) integrates sensors, sensor networks, and cloud for managing sensors, collecting and processing data, and decision-making based on data processed. Though the SCS has received tremendous attention from both academia and industry because of its numerous exciting applications, it still faces the challenge in reliability. The reliability of an SCS is generally referred to as the ability to perform required functions for a given period of time. This work is focused on the <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-terminal reliability of an SCS, which is concerned with the successful communication between all pairs of network nodes belonging to a pre-specified subset <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>. The increased complexity and scale of real-life SCSs require new efficient techniques to evaluate their <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-terminal reliability. In this work we make novel contributions by proposing a network simplification method that can effectively remove all redundant network edges and vertices, leading to a significantly reduced network model for accurate and efficient <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-terminal reliability analysis. The method is based on graph decomposition and reconstruction through articulation vertices. Empirical studies show that the proposed simplification method integrated with the binary-decision-diagrams based evaluation algorithm can significantly speed up <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>-terminal reliability analysis of large real-life SCSs.