The elastic-wave scattering at interfaces, such as cracks, is essential for nondestructive inspections, and hence, understanding the phenomenon is crucial. However, the elastic-wave scattering at cracks is very complex in three dimensions since microscopic asperities of crack faces can be multiple scattering sources. We propose a method for exploring 3D elastic-wave scattering based on our previously developed high-resolution 3D phased-array system, the piezoelectric and laser ultrasonic system (PLUS). We describe the principle of PLUS, which combines a piezoelectric transmitter and a 2D mechanical scan of a laser Doppler vibrometer, enabling us to resolve a crack into a collection of scattring sources. Subsequently, we show how the 3D elastic-wave scattering in the vicinity of each response can be extracted. Here, we experimentally applied PLUS to a fatigue-crack specimen. We found that diverse 3D elastic-wave scattering occurred in a manner depending on the responses within the fatigue crack. This is significant because access to such information will be useful for optimizing inspection conditions, designing ultrasonic measurement systems, and characterizing cracks. More importantly, the described methodology is very general and can be applied to not only metals but also other materials such as composites, concrete, and rocks, leading to progress in many fields.