The discovery of anticancer therapeutics effective in eliminating dormant cells is a significant challenge in cancer biology. Here, we describe new synthetic polymer-based anticancer agents that mimic the mode of action of anticancer peptides. These anticancer polymers developed here are designed to capture the cationic, amphiphilic traits of anticancer peptides. The anticancer polymers are designed to target anionic lipids exposed on the cancer cell surfaces and act by disrupting the cancer cell membranes. Because the polymer mechanism is not dependent on cell proliferation, we hypothesized that the polymers were active against dormant cancer cells. The polymers exhibited cytotoxicity to proliferating prostate cancer. Importantly, the polymer killed dormant prostate cancer cells that were resistant to docetaxel. This study demonstrates a new approach to discover novel anticancer therapeutics.