Is paying for my wife's student loans an exception to reduce the penalty for early withdrawal from my 401(K)?

No.

No, paying student loans does not qualify as an exception to the early distribution penalty for taking a withdrawal from your 401(k).  

 

See the following TurboTax help article for a list of the exceptions in case there is one that you qualify to claim:

 

What are the exceptions to the penalty for an early withdrawal from my 401(k)?

 

@mlock0284