Let M be a module over a commutative ring R, and let T(M) be its set of torsion elements. The total torsion element graph of M over R is the graph $T({Gamma}(M))$ with vertices all elements of M, and two distinct vertices m and n are adjacent if and only if $m+n{in}T(M)$. In this paper, we study the basic properties and possible structures of two (induced) subgraphs $Tor_0({Gamma}(M))$ and $T_0({Gamma}(M))$ of $T({Gamma}(M))$, with vertices $T(M){ackslash}{0}$ and $M{ackslash}{0}$, respectively. The main purpose of this paper is to extend the definitions and some results given in [6] to a more general total torsion element graph case.