We study the properties of three-flavors fermions in an optical lattice in the presence of large threebody repulsion which can be experimentally induced by strong three-body losses. Static and dynamical properties of this system are addressed by using dynamical mean-field theory. The resulting phase diagram shows a strong interplay between magnetization and superfluidity. In the SU(3) symmetric case and in the absence of three-body repulsion, the system undergoes a phase transition from color superfluid to trionic phase, which shows additional CDW modulation at half-filling. This transition is suppressed when including a large three-body repulsion. In this case the color superfluid tends to fully polarize at strong coupling . In the strongly asymmetric case, which is relevant for current experiments on Lithium mixtures, the trionic phase is suppressed by losses and, at the same time, the system is driven to phase separation in the components, which leads to straightforward experimental signatures.