My girlfriend [21 F] cheated on me [23 M] with my grandfather [69 M]. Do I cut my granddad off or try to forgive him?

We have been together for a year.

My girlfriend and grandfather last week set me down to tell me they had a week long affair a couple months ago. They only had sex three times they said, and after the third time they say they both felt extremely guilty and mortified at their actions. They've been wanting to tell me since then but didn't have the hearts. I always knew they got on well, they bonded over many shared interests, but I never saw this coming.
I feel completely sick. I haven't eaten hardly anything since they told me. I haven't officially broken up with her yet, but it is obvious as I haven't responded to any of the texts/calls she's sent. When they first told me and after it had sank in, I left and haven't said a word to anyone outside of work since. I've been a total ghost to my whole family and friend group.

My grandfather and I are very close. For my whole life I have looked up to him. He and my mum divorced when I was a teenager but they have been very friendly to each other which made the process so much easier. I want to forgive my granddad. But if my girlfriend had cheated on me with another person, I would easily cut them both off. And in a weird way my granddad has hurt me so much more by doing this than she has. I could get over a cheating girlfriend. But my relationship with my grandfather, a relationship I cherished, is destroyed. And it's his fault.

My question is this: Should I forgive my grandfather? How can I forgive him? Should I tell my mum or brother? Would I be cruel for completely cutting him off which is what my heart is telling me to do?