TD-27: Can a song that's input via the MIX IN jack or via a Bluetooth-connected smartphone be mixed with the sound of my drum performance and recorded as a mix?

Yes.

Perform the following procedure.
- Refer to “Recording” in the TD-27 Quick Start or Reference Manual (PDF.)

1. Press the [●] button.
   - REC STANDBY screen appears.
2. If the [with Song] indication is shown ("ON") in the lower left of the screen, press the [F1] button to turn it "OFF" (not shown).
3. Use the dial to select “ALL” as the Rec Target.
4. Press the [>/■] button to start recording.
   - You can record for up to approximately three minutes into the unit's memory if there is no SD card, or for up to approximately 60 minutes if an SD card is inserted.
   - To adjust the volume of the smartphone, use the controls of the smartphone itself and the [BACKING] knob.
5. Press the [>/■] button once again to stop recording.