Can you deduct a new vehicle purchase for small business along with also deducting mileage or can I only deduct one or another?

It is a "one or the other" situation.  The IRS terms are Standard Mileage and Actual Expenses.

If you use the Standard Mileage method, you deduct the standard mileage rate for your business miles, plus business parking, business tolls, business local transportation, business portion of the property taxes on the vehicle, and the business portion of interest expense for the vehicle loan.

If you use the Actual Expenses method, you deduct the business percentage of the actual cost of operating the vehicle, plus the business percentage of the depreciation on the vehicle.  Because of special depreciation allowances and what is called the Section 179 deduction, you may be able to write off a significant portion of the business percentage of total vehicle cost in the year it is purchased.

TurboTax will guide you through the best choice for you.  See the TurboTax Help article at this link and IRS Topic 510 Business Use of Car at this link for more information and important details.