High-strength dilute Mg–Y–Zn alloys with cluster-arranged layer/nanoplate (CAL/CANaP) precipitates were developed via combined processes of low-cooling-rate solidification and extrusion techniques. The effects of CANaP morphology and deformation kink bands installation on the tensile properties of the extruded Mg–Y–Zn alloys were investigated. A slow-cooling solidification process with a cooling rate range of 0.1–0.01 K·s⁻¹ produces a CAL-aggregated region in the α-Mg matrix. The CAL-aggregated region comprises long-period stacking ordered (LPSO) nanoplates with an intergrowth structure and the solo-CAL precipitates. The area fraction of the CAL-aggregated region increased with decreasing cooling rate. The microstructure of the extruded Mg_99.2Y_0.6Zn_0.2 alloys prepared from low cooling rate-solidified ingots consisted of three characteristic regions: (i) dynamically recrystallized (DRXed) fine α-Mg grains, (ii) worked coarse α-Mg grains with a CAL-aggregated region, and (iii) worked blocky LPSO grains. The strength and ductility of the extruded Mg–Y–Zn alloys may be controlled by the volume fractions of the worked and DRXed grains, respectively. It is desirable to control the CANaP thickness and spacing to ∼1 µm and ∼0.8 µm or more, respectively, to promote DRX. Conversely, it is necessary to control the CANaP thickness and spacing to ∼1 µm and ∼0.8 µm or less, respectively, to form the worked grains in which kink bands are introduced.