Filing a return through the mail is, of course, the slower of the two processes. For those who mail their federal return, the IRS will remit a tax refund within six weeks after they have been received the completed return. If you file electronically, you should receive your tax refund within three weeks.The IRS allows two options for receiving a federal tax refund: paper check sent via the mail, or an electronic funds transfer (also called a direct deposit). The direct deposit method, not surprisingly, is always the quicker option.iling a return through the mail is, of course, the slower of the two processes. For those who mail their federal return, the IRS will remit a tax refund within six weeks after they have been received the completed return. If you file electronically, you should receive your tax refund within three weeks.