Wrap the ends with electrical tape and replace the cover. Theres a hole in the interior door frame.

How To Hide Wires Cables On The Floor With This Tapping
How to hide doorbell wires. Locate the doorbell transformer which is usually in. Place electric tape around the tips of each wire as you did for the bell wires and push them back into the wall. Remove the screws that are securing the doorbell button to the outside door frame using the screwdriver. Loosen the wire connections with the screwdriver and pull the wires from the button. One photo below is of the doorbell with the cover the other is the doorbell without the cover. If the wires arent long enough to pass through use the extension leads that come with the doorbell.
Remove the plastic sheath to allow about 1 inch of bare wire to show. Pass them through the new hole and out the same hole as the existing button. It will also show you how to conceal the wires and switch to a nest hello doorbell. This video will show you how to relocate a conventional wired doorbell for improved visibility and accessibility. Mounting the pro on the brick right next to it chisel a mini canal through the mortar between the old hole for the bell and the new location run the wires through that canal. Remove the doorbell chime cover and unscrew the wires that supply the unit with power.
The hole comes out on the exterior door frame. Wrap around the wires. Pull the tube apart and wrap around the wires that were tied together. Then connect the wires together with the included wire nuts and push into the hole which you may need to enlarge a little to fit. On the exterior door frame theres another hole which i assumed led the doorbell wires into the wall. As you can see the wires from the the doorbell have been cut.
Strip each side of the wire where you want to make the cuts. 3 twist the wire in your fingers to braid it. Conceal with flex tubing. Use cable ties to bundle cords and snip off the ends as needed. Measure the length of the cords you want to conceal then measure and cut flex tubing to match the length.