The more you use ANYTHING, the closer it gets to the end of it's useful life, but in general, no, there is no limit on how many times you can clone to a drive or how much data you can write to it. If it were an SSD it would be different. Age is generaly the bigger factor when it comes to mechanical hard drives, not amounts.
When in doubt, run something like Seatools for Windows or WD lifeguard tools to check the drive health by running the quick/ short drive self test and the long generic/extended test.