I have paid a student loan garnishment throughout 2019, and was wandering if I can claim that on taxes?

The only thing that is deductible is the interest paid. This is usually reported on a 1098-E.

Please see this answer from JulieH1.

No, the wage garnishment cannot.  That is just repaying a loan. 

However, if you are paying interest on the loan that may be deductible on your return. Student loan interest is interest you paid during the year on a qualified student loan. If you are paying interest on the loan it may be deductible on your tax return as an adjustment to your income if all the following apply:

• Your filing status is any filing status except married filing separately.

• No one else is claiming an exemption for you on his or her tax return.

• You are legally obligated to pay interest on a qualified student loan.

• You paid interest on a qualified student loan.