Summary: A proper total coloring of a graph \(G\) is an assignment of colors to the vertices and edges of \(G\) (together called the elements of \(G\)) such that neighbored elements -- two adjacent vertices or two adjacent edges or a vertex and an incident edge -- are colored differently. The total chromatic number \(\chi^{\prime\prime}(G)\) of \(G\) is defined as the minimum number of colors in a proper total coloring of \(G\). In this paper, we study the stability of the total chromatic number of a graph with respect to two operations, namely removing edges and subdividing edges, which leads to the following two invariants. (i) The total chromatic edge stability number or \(\chi^{\prime\prime}\)-edge stability number \(es_{\chi^{\prime\prime}}(G)\) is the minimum number of edges of \(G\) whose removal results in a graph \(H\subseteq G\) with \(\chi^{\prime\prime}(H)\neq \chi^{\prime\prime}(G)\) or with \(E(H) = \emptyset \). (ii) The total chromatic subdivision number or \(\chi^{\prime\prime}\)-subdivision number \(sd_{\chi^{\prime\prime}}(G)\) is the minimum number of edges of \(G\) whose subdivision results in a graph \(H\subseteq G\) with \(\chi^{\prime\prime}(H)\neq \chi^{\prime\prime}(G)\) or with \(E(H) = \emptyset\). We prove general lower and upper bounds for \(es_{\chi^{\prime\prime}}(G)\). Moreover, we determine \(es_{\chi^{\prime\prime}}(G)\) and \(sd_{\chi^{\prime\prime}}(G)\) for some classes of graphs.