Checkpoint-blockade immunotherapy enables the patient’s immune system to recognize tumor cells that were previously invisible due to immune escape, but these therapies lead to heterogeneous patient outcomes. Focusing on colorectal cancer, in which two subtypes have markedly different responses to immunotherapy, we seek to understand how the mutagenic landscape of the tumor is related to therapeutic outcomes. First, we model neoantigen evolution in growing tumors using a stochastic branching-process model. Neoantigenic peptide sequences arising from colorectal cancer patient data are scored for fitness, giving each in-silico tumor a unique pre-treatment mutational landscape. Next, we use a dynamical systems model of the tumor-immune interaction under checkpoint-blockade therapy, optimized by fitting clinical trial data to model outcomes, to simulate therapeutic trajectories. We relate therapeutic outcomes to the heterogeneity of tumor mutational landscape, quantified by the number of mutations in the tumor, the immunogenicity of these mutations, and the clonality of the neoantigens present in the tumor. A high mutation burden, as well as the presence of highly fit neoantigens, are not sufficient to determine a successful response to therapy; conversely, the presence of a strong clonal neoantigen, present in every cell of the tumor, appears crucial for a successful response to therapy.