Single-cell assay of transposase-accessible chromatin sequencing (scATAC-seq) unbiasedly profiles genome-wide chromatin accessibility in single cells. In single-cell tumor studies, identification of normal cells or tumor clonal structures often relies on copy-number alterations (CNAs). However, CNA detection from scATAC-seq is difficult due to the high noise, sparsity, and confounding factors. Here, we describe AtaCNA, a computational algorithm that accurately detects high-resolution CNAs from scATAC-seq data. We benchmark AtaCNA using simulation and real data and find AtaCNA's superior performance. Analyses of 10 scATAC-seq datasets show that AtaCNA could effectively distinguish malignant from non-malignant cells. In glioblastoma, endometrial, and ovarian cancer samples, AtaCNA identifies subclones at distinct cellular states, suggesting an important interplay between genetic and epigenetic plasticity. Some tumor subclones only differ in small-scale (10-20 Mb) CNAs, demonstrating the importance of high-resolution CNA detection. These data show that AtaCNA can aid in integrative analysis to understand the complex heterogeneity in cancer.