You dont fire people for a living. I work in HR. I have known one company employee someone in a role similar to this. Their role was to manage redeployment, if one of our clients scaled back the contract or stopped using us completely. That often had grievances and loss of jobs, as often they couldnt redeploy people to something that suits.
Your job is to over see grievance process and redundancy. Redundancy is not firing someone. If you are overseeing the grievance process to see if it's done correctly, then you simply manage grievances.
I used to manage grievances. The only time they ending in firing was when the person who was subject of the grievance was found to have done something that was gross misconduct.
Does you company really have enough of these cases to employ someone just to do that? Grievances relating to Gross mis conduct cases?
What about when its gross mis conduct but no grievance is opened? It's simply been witnessed and a company has suspended and investigating?
HR do all these roles and more. Manage disciplinary, grievances, redundancy......plus other roles as well. Your job is to manage these. Not to fire people. I would be very concerned that someone in your position felt their job description was to fire people.
As a people manage and working in HR part of my role, is firing people, if required. That's not actually my role. It's a very small part of my responsibilities. It's quite an awful part of the job, its not a nice thing to do, even if the person has done something wrong.
The only time I havenet felt a bit bad was when a man had been over heard making comments so disgusting to a young woman, it was sickening and sent her emails and instant chat saying similar. The things he said, ended with police involvement. It was scary as fuck. It still wasnr nice. The young woman was so shaken by it. I felt desperately sad for her that she had been subjected to this.