I cashed in a traditional IRA in 2017 and am being taxed on the full amount. Is there any way I deduct the IRA amount in the year that I took out the IRA?

You can only amend to get a refund for up to three years. If you never deducted the IRA contribution, then you have nondeductible IRA contributions. There would be a Form 8606 that would keep track of those contributions over the years. Distributions from a Nondeductible IRA are not taxable.

We'll automatically generate Form 8606 (Nondeductible IRAs) if you reported:

• Nondeductible contributions made to a traditional IRA;
• Distributions from a traditional, SEP or SIMPLE IRA that had nondeductible contributions (excluding rollovers, conversions, recharacterizations, qualified charitable distributions, one-time distribution to fund an HSA, or return of certain contributions);
• Conversions from a traditional, SEP, or SIMPLE IRA to a Roth IRA; or
• Distributions from a Roth IRA (other than rollovers, recharacterizations, or a return of certain contributions).

You would be asked this question after you have entered your 1099-R for your IRA distribution.

The screen sequence would be as below:

• What Did You Do With The Money? Cashed out
• Any Nondeductible Contributions to Jason's IRA? Yes
• Let's Find Your IRA Basis.
• Tell Us the Value of Your Traditional IRA

Simple answer: no. 

When you withdraw from an IRA, the entire amount is subject to tax in the year you took the distribution. None of the amount in box 1 of your 1099-R is deductible, UNLESS there is a different amount in box 2a. Even then, you don't actually take a deduction, you just report the taxable amount differently. TurboTax (TT) handles that automatically.

If you made some non-deductible contributions to your IRA, over the years, some of the distribution will not be taxable. Again, TT will handle that in the 1099-R interview.