I cannot make much from that picture (needs to be in wire-frame mode - before and after to be sure).
But if you say the mesh is getting ripped with sculpting/smoothing, then it means mesh was already ripped when imported.
Happens a lot when 2 vertices occupy the same space and not joined together.
What you can do, is to go Mesh>Weld Vertices, specify a relative distance between vertices (0.01 is good enough for "perfectly" spaced double vertices) and click Merge.
But do it right away upon importing an object.