I assume you are talking about a 2018 1099.  If not, let me know in a comment below.

Also, if you have already filed your tax return and received a 1099, let me know in a comment below as well.

The taxes you owe are based on your entire tax situation.  So, you don't really owe taxes on a 1099 alone.  You owe taxes based on all your taxable income after all your income and deductions are considered.

If you have taxable income on a 1099 and taxes were not withheld, your tax liability will be higher at the end of the year than it would be without the 1099.  So, if you had a refund without the 1099 income, yes, that refund will be reduced to cover the increase in your tax liability when you add the 1099 income.   Your refund might go down / be completely diminished or you may run into a tax liability situation (where you have to send the IRS money instead of getting a refund).