Yes, you can use TurboTax for 1099 and W-2 income and to deduct your related expenses.   If this is income for your multi-member LLC business, you will want to use Turbo Tax Business.  If it is your personal self-employment income or a single member LLC, see below to report on Schedule C on your personal tax return. 

TurboTax Self-Employed will handle income and expenses for both W-2s and 1099s for a single-member LLC.   

Self-Employment expenses are reported on Schedule C; these are the expenses related to your 1099 income.  Under Business Expenses, you will see the following: 

Business Expenses (Everyday expenses conducting business) 

• Business Vehicle Expense - actual or standard mileage
• Other Common Business Expense - supplies, utilities, office rent (that's not part of your home)
• Home Office Expense 

For any expenses that are related to your W-2 income, they are no longer deductible.  Under the Tax Cuts and Jobs Act (TCJA) that Congress signed into law on December 22, 2017, the unreimbursed employee expenses deduction has been suspended in tax years 2018 through 2025. If you’re self-employed or own a business, enter your business-related expenses on Schedule C instead.

[Edited 04/12/20 to reflect current law for Form 2106]