Of course, a nuclear reactor produces heat, not electricity directly, so we're limited by the Carnot cycle, and will need large radiators, defeating some of the mass savings. OTOH space is very cold, and a suitable gas can be made to work with a seriously higher temperature difference than practical on Earth, giving better utilization of the heat. OTOH reaching the asteroid belt and Jupiter in reasonable time is only possible with non-chemical rockets, and nuclear fission power is the only realistic option now.

Nuclear fusion is another feasible option, if you can get around the Partial Test Ban Treaty because an asteroid is going to exterminate humanity or something.

Such a device, while possible, is very fuel-inefficient: you need several kg of plutonium just to ignite the tritium. Peak mechanical and radiation loads are very high.

A thruster which could produce much lower thrust for a much longer time seems much safer and cheaper to implement, even if detonating nuclear bombs in space were not an issue. And a issue it is: you need to do it rather far away from all other spacecraft, which means some weird orbital plane.