Static mixers play an important role in industrial applications such as polymer processing, where they are used to increase flow homogenization in viscous fluids, e.g., to achieve a more uniform distribution of material or temperature. The porous structure of the mixer induces flow deflection, facilitating mixing and heat exchange. In this contribution, we report on numerical design optimization of static mixers. Key to the design method is a combination of isogeometric shape optimization and lattice structures. The latter are constructed using a spline-based functional composition, a concept originally introduced in [1]. The geometry is built from microtiles, which are embedded into a volumetric spline that outlines the external geometry. The ability to modify the global shape as well as the building blocks, the microtiles, provides a large variety of achievable geometries. Utilizing isogeometric analysis (IGA) is motivated by the spline-based geometry description. Originally proposed in [2], IGA aims to bridge the gap between geometry construction and analysis by using the same representation for both. Time-consuming and computationally intensive geometry preparation and meshing are significantly reduced. For the optimization, we employ a gradient-based optimization algorithm. Due to the many design variables addressing both the microtiles and the macro-structure, adjoint methods to compute the gradient are essential. In this contribution, we will detail the developed method and demonstrate its capabilities on a test case.