To help save on my utility bill I usually cut my hot water heater off doing the day for
8 to 10 hours. I cut it off when its not cycling to heat up. I would like to know by doing
This, would it cause any problems with the heating element, thermostat or electrical?
Thank you in advance.

If you are doing this at the breaker panel, you will wear the breaker out a bit earlier than it should. Most breakers are not made to use regularly as a switch. There are breakers that are made for regular switching. If you go to a good electrical supply house you might be able to get an exact replacement for your breaker with the switch rating. Can't help you with models and/or model suffixes, I have never had to install one of those.

Other than that, you won't hurt your water heater. You probably won't save much money either. Modern water heaters are insulated very well and don't lose much heat in 8 hours of idling. I would recommend shutting it off only if it will be off a day or more. You will get much more bang for your buck if you carefully insulate several feet of the cold water line into the heater and any hot water lines that you can see. Double insulate them if you are really anal.