Model-based diagnosis (MBD) has been widely acknowledged as an effective diagnosis paradigm. However, for large scale circuits, it is difficult to find all cardinality-minimal diagnoses within a reasonable time. This paper proposes a novel method that takes a significant step in this direction. The idea is to divide a circuit into zones and compute the cardinality-minimal diagnoses by finding subset-minimal diagnoses with cardinality-minimal via a maximum satisfiability (MaxSAT) solver on an abstracted circuit that is composed of these zones instead of all components. We also propose a new propagate-extend method for extending the seed-TLDs to obtain all cardinality-minimal diagnoses efficiently. We implement our method with a state-of-the-art core-guided MaxSAT solver, and present evidence that it significantly improves the diagnosis efficiency on ISCAS-85 circuits. Our method outperforms SATbD, which was recently shown to outperform most complete MBD approaches using satisfiability (SAT).