Predicting tumor dynamics in biological systems under physiologically relevant conditions using mathematical and computational models remains a challenging problem. Among the various approaches proposed to govern tumor dynamics, continuum models based on phase-field (diffuse-interface) formulations have proven to be an effective modeling strategy for describing the dynamics and interactions of multiple species. Within its framework, this work presents a tumor growth model based on the Cahn–Hilliard equation. The formulation involves a fourth-order differential operator that imposes higher continuity requirements on approximation spaces for a well-defined primal variational formulation. We use isogeometric analysis (IGA), which inherently satisfies this requirement through spline-based basis functions within a unified geometric and analysis framework. IGA further eliminates the need for mixed or auxiliary-variable approaches commonly used in standard finite element discretizations. In particular, a locally adaptive IGA scheme with hierarchical B-splines is used to reduce computational cost while maintaining accuracy, since phase-field models generally demand fine meshes to resolve steep gradients at phase interfaces. The model is first evaluated on standard benchmark cases and then applied to an organ-scale, patient-specific geometric model of the breast reconstructed from magnetic resonance imaging (MRI) data. Our results show that the model reproduces known tumor morphologies, ranging from a spheroidal pattern to fingered growth. A series of numerical experiments further shows the diversity of tumor dynamics produced by different model parameter choices. Taken together, the findings demonstrate the predictive potential of the Cahn–Hilliard phase-field tumor growth model integrated with a locally adaptive IGA framework.