Independent contractors who file schedule C can still deduct work-related mileage. If the payment is included in your taxable income, then you can fully deduct your car expense against that income, using the standard mileage method or the actual expense method. (The standard mileage rate method is usually more lucrative.) Of course, this assumes you have accurate records of the date, time, mileage, and business purpose of each trip.
Your mileage from home to the grocery store at the beginning of your work day, and from the last customer's home to your home at the end of your work day, is not deductible.
This is covered in publication 463, chapter 4. Although the publication is not yet updated for 2018, the deduction for self-employed workers has not changed.
https://www.irs.gov/pub/irs-pdf/p463.pdf
