Treat each road as an edge with capacity . The maximum flow from to equals the maximum number of edge-disjoint paths from source to destination. By max-flow min-cut theorem, the minimum cut capacity equals the max flow.
Since capacities are , the min cut is the minimum number of edges to remove. Compute max flow using Dinic or Ford-Fulkerson. The flow value is the answer to the question: how many roads must be blocked?