I don‘t think, that you can read the SAML response in AEM directly. But you could configure the AEM SAML Service to map a few SAML properties to AEM user profile properties that you than can read.
If you want to know what‘s in the SAML conversation, I would use special browser plugins (look for SAML tracer or SAML debugger in your browsers extension/plugin store). Theses Plugins filter SAML traffic from other traffic and do the necessary decoding for you.