I tweaked a little bit based on the understanding of Elias's fragmented sphere example. I wanted the extruded fragments triggered by mouse to be a enclosed shape. Therefore, I need to extent the vertex which shared with the intersected face as well.
Code hosted in the codeSandBox.
So the result looks like this:
However, it didn't cover the indices that didn't share with them but still were part of the side faces.
Also, I wanted to detect the neighborhood faces around the intersected face but didn't know how. Any suggestions?