Not well. Polyurethane does not cleanly melt-cut the way polystyrene does — instead of slicing, a hot wire tends to char, gum and smoke, leaving a rough, sticky edge and nastier fumes. PU is better worked with knives, saws, sanding or CNC routing.
Hot-wire cutting really wants thermoplastic foams that melt at a low, controllable temperature — EPS and XPS are the sweet spot. If you specifically need PU (for its toughness or finish), cut it mechanically and reserve the hot wire for polystyrene. As a bonus, avoiding PU also avoids its messier smoke; keep any hot-wire work to EPS/XPS and ventilate regardless.
Hot-wire cutting really wants thermoplastic foams that melt at a low, controllable temperature — EPS and XPS are the sweet spot. If you specifically need PU (for its toughness or finish), cut it mechanically and reserve the hot wire for polystyrene. As a bonus, avoiding PU also avoids its messier smoke; keep any hot-wire work to EPS/XPS and ventilate regardless.