Yes, you can deduct food and veterinary care expenses for service animals. This is a medical expense on schedule A. To receive any actual tax benefit, you must itemize your deductions and your total itemized deductions must be more than the standard deduction. Many people with modest medical expenses never receive a tax benefit for them.
Because this is a tax deductible medical expense, the same costs would also be eligible to be paid from a health savings account (HSA) or a medical care flexible spending account (FSA) if you are eligible to participate in those programs.