From a sandbox org I am included in an email alert for Milestone breaches that I no longer want to receive.
How can I stop the org from sending this to my account?
You need to find the right entitlement process and edit the milestone actions. But i think that for this you will have to create new versions of those. Which means that the old entitlements will still have the old version. You can update the version on entitlements, but not for all, there is some validation about open cases with those entitlements.