As noted by the Sixth Doctor, mourning was represented by the colour blue on "a number of civilised worlds" including Necros, but notably not Earth. As such, he wore a blue coat as a mourning suit. (TV: Revelation of the Daleks, WC: Real Time/AUDIO: Real Time)
The Ninth (TV: Father's Day) Tenth (TV: The Age of Steel) and Twelfth Doctors felt that mourning ought to wait until the danger was over. (TV: Mummy on the Orient Express) The Tenth Doctor urged everyone, for the time being, to "move on" from the death of Ricky Smith whilst London was still under attack by Cybermen. (TV: The Age of Steel) The Ninth Doctor emphasised survival, telling Stuart Hoskins he could mourn for his father later, but that he should focus first on staying alive. (TV: Father's Day) The Twelfth Doctor refused Perkins the chance to take a moment to mourn the loss, seconds before, of Hector Quell, saying:
No, no, no. We can't do that. We can't mourn. People with guns to their heads, they cannot mourn. We do not have time to mourn.
After Adric's death, the Fifth Doctor, Nyssa and Tegan agreed that they would miss him, but the Doctor insisted that he "wouldn't want [them] to mourn unnecessarily". The Doctor opted instead to attempt to take his companions on a trip to the Great Exhibition of 1851, in order to "cheer [them] all up" and take their minds off the grief which they shared. (TV: Time-Flight) At first Nyssa thought he was being "frightfully cold-hearted", but she came to understand in time that he had no choice but to hide those emotions, as the Doctor felt his loss harder than anyone. (AUDIO: Tartarus)
Edith Thompson was not allowed to mourn after the death of Charley Pollard aboard the R101. While the rest of the household mourned her loss, Edith had to keep to her duties as cook. Charley had been the only one who was kind to her. As a result, in an aborted timeline, Edith committed suicide. (AUDIO: The Chimes of Midnight)
Large-scale, even planetary-level mourning could be expected following certain tragedies, like the crisis at Bowie Base One. (TV: The Waters of Mars) Rani Chandra felt that the whole world should be mourning the Doctor when it was believed he was dead. (TV: Death of the Doctor)
Though the Fourth Doctor described them as non-sentient, Drashigs mourned their dead. Trencher recognised the sound they made while doing so, having heard it only once before. Vanessa Seaborne, who was connected to the Drashigs, felt their loss after the death of the Alpha. (AUDIO: Planet of the Drashigs)