How to measure a signal generator with an oscilloscope probe?
Don't do that. Oscilloscope probes aren't just plain wires that lead back to the scope's BNC input. Connect the signal generator to the breadboard, then connect the scope probes to the breadboard too.

Don't cut the BNC connector. Buy a pre-made one with the clips you want. Being coaxial cables, BNC cables are not straightforward to just cut into and connect something else to it.