MOTIVATION: Dimensionality reduction for single-cell RNA-sequencing (scRNA-seq) data involving multiple biological samples presents a significant analytical challenge. RESULTS: We introduce MUlti-Sample Trajectory-Assisted Reduction of Dimensions (MUSTARD), an innovative trajectory-guided dimensionality reduction method specifically designed for multi-sample, multi-condition scRNA-seq data. By integrating pseudotemporal information, MUSTARD provides a comprehensive unsupervised approach that simultaneously captures major gene expression variation patterns along pseudotime trajectories and across multiple samples, facilitating the discovery of biologically meaningful sample heterogeneity, endotypes, and associated gene markers and modules. In data-driven simulations, MUSTARD outperformed existing methods in distinguishing sample groups, achieving superior out-of-sample prediction accuracy. In two COVID-19 datasets and a tuberculosis dataset, MUSTARD identified components linked to symptom severity, batch effect, and other known biological variations, with notable overlap in immune response genes across the two independent COVID-19 datasets. These results underscore MUSTARD's flexibility and power in identifying biologically relevant sample heterogeneity across diverse datasets. AVAILABILITY AND IMPLEMENTATION: The R package MUSTARD with a detailed user manual is publicly available at https://github.com/haotian-zhuang/MUSTARD and Zenodo (DOI: 10.5281/zenodo.18293392). The source code to reproduce the results in this paper is available at https://github.com/haotian-zhuang/MUSTARD_Paper and Zenodo (DOI: 10.5281/zenodo.18293392).