This effect usually requires modifying a vertex shader to send the individual triangles of a mesh flying in whatever patterns you need for the particular look. Some examples that include source code, in order of simplest to most complex:
- https://github.com/Jam3/jam3-lesson-webgl-shader-threejs#step-4-exploding-triangles
- Explosion effect in textGeometry
- https://tympanus.net/codrops/2019/03/26/exploding-3d-objects-with-three-js/
The last requires some modeling knowledge with programs like Blender or Cinema4D, to prepare the particles into which the mesh will be broken.