Am I able to claim wages that were garnished for student loan repayments?

Claim your garnished wages for what?   Your wages are reported on your W-2 and you need to enter your W-2 exactly as it appears.   If you paid interest on the student loans and can discern how much of the garnished amount was for the interest that is all you can ever claim for paying a student loan.

No. Although, you are able to deduct the interest portion of these payments if you were given an interest statement or Form 1098-E that shows the interest paid, and you otherwise meet the requirements to deduct student loan interest. 

is there a place I can access my 1098-E if I don't have a paper copy?

Try going online with the lender who holds the loan.