In Volume 1, Mio cries during her Heroic BSoD when she thinks Kazuki has forgotten about her after he defeats her in their duel. Then, she returns to her room and remembers her loneliness when Kazuki left her five years ago.
The death of Mio Amasaki at the hands of Loki towards the end of Volume 1.
She gets slashed through the chest while taking the full force of Loki's attack in a Heroic Sacrifice and collapses in Kazuki's arms. Kazuki understandably goes berserk and manages to wound Loki, only for Kazuki to get knocked down in response and Kaguya has to step in to rescue him.
After Loki pulls a Villain: Exit, Stage Left at the end of his fight, Mio tells Kazuki that she was happy she could meet her, apologizes for her earlier actions and asks him tokiss her on the lips while bleeding profusely. Then, she's gone, just like that. It's sad knowing that they have just reconciled after their duel earlier on in the volume.
Kazuki's reaction to her death. He lets out an anguished Death Wail and brings Mio Back from the Dead using her Revive spell by kissing her on the lips.
Hibiki abandoning Kazuki in front of the Nanohana Institute was heartbreaking, especially when you learn about her death.
Nyarlathotep's experiments in changing selected humans to elves.
In Volume 3, Koyuki tells Kazuki about her loneliness. All the more heartbreaking when you learn that she was one of the test subjects who was frequently subjected to Fantastic Racism by everyone else, including her own parents.
Miyabi's persecution after being transformed into an elf as one of Nyarlathotep's test subjects. It's so bad that Shinobu was even devastated by it.
Think about Nyarlathotep's experiments from an Elf's perspective. You were selected and subjected to cruel experiments that will eventually change your eyes to red and your hair to silver. Then, you're suddenly subjected to Fantastic Racism from everyone due to the rarity of your race and being ridiculed frequently by others. You've gone from a normal human to a misunderstood species. Imagine how that would feel.