I planted a peach tree on my front yard two years ago

I have not paid much attention to it since them (yes I know it is all my fault

Now I decided to prune it.
I read a couple of brochures on it, and decided to do during long weekend.
All of the sudden I have realised that I have two big branches running from the tree trunk below the graft union

At least it looks like that to me. I can be wrong so I would appreciate if you could take a look at the photos below.
Those two branches are much bigger that the one running from the graft union.
So I have two questions :
1. do I really have that problem - branches from the tree trunk below the graft union ?
2. if so, what do I do ? Just cut them off with a saw ?
Thank you.
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