During which phase of the autopsy would swabs of the mouth be taken?

The phase of the autopsy where swabs of the mouth would be taken is Records of Specimens Retained and Examinations performed.

There are 10 steps in doing an Autopsy. These steps are called Autopsy Protocol. Here are the 10 steps.

1) Preliminary Procedures
 2) Summary of Known Circumstances
 3) Documents Reviewed And/or Evidence Examined
 4) External Examination of Body
 5) Victim Identification Procedures
 6) Internal Examination of Body
7) General Description of Body Organs
 8) Specific Description of Wounds or Injuries
 9) Establish Evidential Chain-of-custody
10) Record of Specimens Retained and Examinations Performed

Swabbing of the mouth is in the last step of the Autopsy Protocol.