Surprised is used with BY in this case. We are surprised by something.
I was surprised by the news.
He crashed the car because he was surprised by a deer.
We don't usually use WITH unless it's a surprise that someone organized for us.
His friends surprised him with a birthday party.
My parents surprised me with a new puppy.
In this case the preposition WITH comes after the object
E.g : he surprised ME with..... We surprised HER with...
Hope this helps!