Billy,
No, your clutch should not grind the gears. It depends on how your clutch is adjusted......which yours sounds like it needs adjustment. Here is a quick check you can do to determine that......while running your cub, depress the clutch pedal and hold it for a minute or so....at least 30 seconds (count it out), then try to shift into a gear. Chances are that it won't grind. I think your driveshaft is still spinning while you are still trying to shift, even though your clutch pedal is depressed and that is what is causing the grinding sound. You can adjust your clutch braking as described above and as described in your owner's manual to stop the driveshaft faster once you depress the clutch pedal. Hope this helps.
Oh, I would change out my transmission fluid regularly as moisture can sometimes build up and prevent it from performing properly or doing damage. It does cost a little, but really what are your tools/equipment worth to you? Proper/preventative maintenance can save you big $$$ in repair bills!!!
Cub Cadet 123