Clipboard manager for Mac that doesn't use any cloud service
I use Copyclip. It remembers a certain amount of clips. You can also blacklist apps from which it should not clip something, for instance password managers.
It does not use any kind of cloud. It is only local.

To verify that it does not use any cloud services. You can block the app from accessing the internet. OS X Firewall or third party app. Or you can check all established internet connections with:

lsof -i | grep -E "(LISTEN|ESTABLISHED)"


Or trust the developers that they have not put any hidden cloud abilities into the app. Or use some OpenSource app and check the code. Or develop yourself.