The source text is of poor quality and was probably not written by a native speaker."

Now I understand the warning about your sarcasm to me.
"Your sarcasm to me" is incorrect. Possible alternative is:
Your sarcastic attitude (to me).

"Manipulation of a psychologist's mind?"

"Please, spare my head, dear surgeon, I need something up on my neck to understand you."

I need something up on my neck to understand you.

Up on my neck is incorrect. Upon my neck, or on my neck, is correct.

The normal expression is "a head on my shoulders" not "a head on my neck".

The speaker means that he/she will need his/her head in order to understand the psychologist.