The "date deployed" is the day you left, however, if you were deployed in 2016-2017, enter 01/01/2017 as the date deployed - for a 2017 tax return, only dates in 2017 are relevant for this question.
In any case, your answer to this question won't affect your taxes. It will only affect the order in which the program asks other questions pertaining to your military service. Your DFAS Form W-2 will account for any tax breaks you get while being deployed.