We propose a new algorithm for practically feasible exhaustive generation of small multiway cuts in sparse graphs. The purpose of the algorithm is to support a complete analysis of critical combinations of road disruptions in real-world road networks. Our algorithm elaborates on a simple underlying idea from matroid theory – that a circuit-cocircuit intersection cannot have cardinality one (here cocircuits are the generated cuts). We evaluate the practical performance of the algorithm on real-world road networks, and propose algorithmic improvements based on the technique of generation by a canonical construction path.