While the mirror's frame is face down on the table, remove your router from the router table and change the bit to a rabbeting bit with a bearing tip. This will be used to cut a 3/8" wide rabbet around the inside of the back of the frame.
The finished depth of this rabbet should be the same (or ever so slightly deeper) as the depth of the beveled edge of your mirror that will fit into the frame. Adjust the depth of your bit appropriately before routing the rabbet.
After completing the rabbet with the router, you'll be left with rounded corners that will need to be cleaned up with a sharp chisel. Place the mirror into its final position to make sure that the mirror will fit properly. Be sure that the rabbet is slightly wider than the mirror to accommodate any expansion that the wood might encounter over time.
TIP: Because of the open grain of oak, it is very easy for chunks of stock to tear away when routing. As such, when working with oak, it is imperative that your router bits are extremely sharp. Additionally, it is better to route in very shallow increments so that the bit is much less likely to grab and tear the stock. If your desired depth of the rabbet for the mirror is 1/4", make the first rabbeting pass at 1/8" deep, then re-adjust the depth of the bit to the final 1/4" depth and make another pass. Move slowly and evenly as you work around the oak frame.