While printers are widely regarded as trusted peripherals, their internal mechanical execution reveals subtle vibrational patterns that can leak document structure. We present VibraPrint, a passive mmWave sensing system that infers high-level document attributes—such as page count, content density, and template type—as well as finer-grained structural cues including line count, per-line text amount, and average word-length trends. These properties emerge because layout-induced actuation patterns imprint low-frequency vibrations on the printer chassis, which are remotely captured using a 60 GHz radar without accessing content, print commands, or firmware. To extract meaningful structure from weak and heavily filtered signals, VibraPrint employs a two-stage recovery pipeline that combines global arc fitting with rhythm-aligned segment-wise refinement. Each segment is encoded using hybrid time–frequency features and processed by a structure-aware Transformer for multi-task inference. Evaluated on 500 print jobs across 20 printer models, VibraPrint achieves a mean page-count error of 1.05, over 90% accuracy for density and template prediction, and reliable estimation of per-line structure under distance and alignment variations. These results reveal a previously unrecognized class of structural side-channel leakage inherent to everyday printing workflows.