Slags containing critical minerals concentrated in artificial phases, so-called engineered artificial minerals (EnAMs), are a novel source of critical raw materials. To liberate the EnAMs, the slags need to be comminuted, reducing the size of the particles. This work investigated the dependence of the breakage behavior on particle size and mineral structure during the comminution of an EnAM-containing slag. Piston-die experiments were performed for particles in the 3 mm to 5 mm size range. Nanoindentation and two-roller breakage tester experiments were performed for those in the 50 µm to 200 µm size range. The investigations were accompanied by X-ray computed tomography (XCT) and scanning electron microscope/energy dispersive X-ray spectroscopy (SEM/EDX) measurements as well as a micro X-ray fluorescence analysis to examine the mineral microstructure. It was found that the commonly assumed exponential connection between particle size and strength differed in the two size ranges. This behavior can be linked to different grain and cluster sizes, which were found in the investigation of the mineral microstructure. In addition to particle size, it was found that mineral structure plays an important role when characterizing the breakage behavior.