If I have uncompensated losses due to hurricane damage, can I deduct the losses from my taxes?

That depends on what kind of losses.

Lost property, or lost property value (such as damage to home, contents, and vehicles) can be taken as a casualty deduction.  There are some rules and requirements for determining the amount of loss you can deduct, see the rules and instructions for the form.  And if you have insurance coverage but don't file a claim, you can't claim any loss that would have been covered.

The loss you can deduct is the decrease in fair market value, but no more than your original cost.  You can't deduct for replacement cost.  For example, if you had a total loss of an uninsured car that cost $25,000, had a blue book value of $10,000, and a replacement will cost $35,000, the deductible loss is $10,000.  

You can't deduct lost wages, the cost of temporary lodging, or other expenses related to the incident. This is noted on page 10 here.https://www.irs.gov/pub/irs-pdf/p547.pdf