Watertight remeshing aims to recover a surface that induces a globally consistent interior--exterior partition of 3D space. However, for meshes with complex topology, single-layer structures, or large missing regions, inferring such a partition from local surface geometry is inherently ambiguous. As a result, existing methods often produce surface-accurate yet volumetrically inconsistent reconstructions, e.g., closely spaced double shells. The key insight of this work is that watertight remeshing should be treated as a volumetric partitioning problem rather than a surface-level repair task. To this end, we propose CelloCut, a constructive framework that formulates watertight conversion as a binary labeling problem over a Delaunay tetrahedral partition of space. We solve this via graph-cut energy minimization with one-sided constraints that preserve proxy-supported interior evidence and weighted interface penalties that discourage unsupported newly introduced boundaries. By computing a globally consistent volumetric partition, CelloCut guarantees a strictly watertight output by construction and strongly suppresses pseudo-watertight artifacts such as double shells, even under severe topological defects. Experimental results on two newly introduced challenging benchmarks, CelloScan and CelloFill, as well as standard ModelNet10 dataset, demonstrate that CelloCut significantly outperforms state-of-the-art methods, particularly in handling complex topologies and single-layer structures, producing compact and volumetrically consistent solid reconstructions. The project page is available at https://rangeryx-66.github.io/CelloCut/.

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