Algorithm - Find Min Cut

$1.$ Compute max flow from $s$ to $t$ using any max flow algorithm (Dinic, Ford-Fulkerson, etc.).

$2.$ Build the residual graph after max flow. Include edges with remaining capacity.

$3.$ Run BFS/DFS from $s$ in the residual graph to mark all reachable vertices as $S$.

$4.$ All other vertices form $T$. These are unreachable from $s$.

$5.$ Edges from $S$ to $T$ in the original graph form the minimum cut.