I work as a full time school teacher and travel to tutor students after school each day. Can I claim the mileage from my school to my first student of the evening?

Is tutoring your business from which you get self employment inc?

W-2 employees can't deduct mileage on their federal return.   Some state do allow a deduction for unreimbursed job expenses.    

If your tutoring activities are a side job that you receive self-employment income for, you can claim mileage for that work on Schedule C.   Commuting miles are never deductible.  

The IRS classifies the following trips as tax-deductible:

• Driving between two different workplaces 
• Driving from your home to a temporary workplace (a workplace is generally defined as temporary if you expect to work there for less than one year)
• Meeting clients and visiting customers
• Running business-related errands

The types of trips that aren’t considered business and are not deductible:

• Commuting to and from your home to your permanent workplace
• Commuting to and from your home to a second workplace

See the IRS Infographic in Figure B - When Are Transportation Expenses Deductible?

Auto-Related Tax Deductions