I filed for an Amended Federal Tax Return. I received an email that this was approved by the IRS. I wanted to receive my refund via wire. Why does it say it's mailing it?

You can try calling the IRS to see if you can change your direct deposit info.   

Even though you entered your bank info in your original return, it may not have transferred automatically to your amended return. 

Here's more info about Updating Your Direct Deposit Info with the IRS.