If my wife owes student loans will they take my tax return if we file separately?

No, they generally will not be.  If you are not responsible for the loans, and you were not married when they were incurred, then filing separately is one option that is available to you.  However, there is also a second option:  filing as an injured spouse.  

When you file as an injured spouse, you still get all of the benefits that are available in a joint filing (credits and deductions that are not allowed when filing Married Filing Separately).  You can choose this option by including Form 8379, Injured Spouse Allocation.  Here is an FAQ that discusses how you can prepare the Form:  https://ttlc.intuit.com/replies/3326788

Filing as an Injured Spouse is the best option if you both have income and you wish to protect as much as possible of your refund.  The IRS does make the final determination, however.  They will determine the part of the refund that was generated from your wife and the part that was generated by you.  Your wife's portion is offset, or applied, to her debt, and your portion is still refunded.  This is the way you can still pay significantly towards the debt while at the same time still receiving a decent portion of refund.  (While it is possible to receive some additional refund with you filing separately, she will pay very little towards her debt and may even owe.)

You are not required to file this way; you may file separate if you choose.  However, you should at least consider the option.

If your wife still owes these funds, you should consider filing Form 8379 again with your return this year. 

If denied, you will have the right to appeal, which will be outlined in any denial letter you receive.

Be aware that there may be strict deadlines for appeal.

For more information, please see the IRS's Appeals page.