It is quite common for this to happen for a number of reasons. You pay taxes on your total income, not based on each W2 (or income) entry. The first cause is due to the way the standard deduction and personal exemption works in our taxing system. If you are married, then the first $20,800 of your income is not taxed because of standard deduction ($12,700) and your personal exemption ($4,050 x 2). TurboTax automatically applies these deductions right off the bat.
So, when you entered your W2, you likely didn’t pay tax on a good portion of that income, which leads to getting more of your Federal withholding back. But, then when you added your wife's W2, your taxable income increased as well as your tax liability. So, instead of being able to get more withholding back, you had to use it to pay tax.
Also, as your taxable income increases, you may even get placed into a higher tax bracket. You may also lose eligibility for income-based tax credits such as the Earned Income Credit or lose the ability to claim certain deductions as your income increases.
When you file separately, you only get half of the deductions and exemptions listed above, your tax rate is higher, and you are not allowed to claim certain deductions and credits. For most people, filing separately results in more tax due, not less. But, if you still want to compare, then you would need to create a separate, new account online and basically run through the whole return for each spouse separately.
You can read more about MFJ vs MFS at the link below -