Who are the other two girls whose hair Araragi has cut? In the last episode of Hanamonogatari, near the end of the episode where Araragi prepares to cut Kanbaru's hair, he said "You are the third girl whose hair I'm cutting".

Who was the other two girls that got their hair cut by Araragi?
One of the two girls is Hanekawa Tsubasa. Remember that during the events in Karen Bee1, she underwent an image change where her usual braided hair was replaced by bob cut, and her glasses replaced by contact lens. Her hair was actually cut by Araragi when she went out with him to karaoke in the short story Tsubasa Song2, which takes place some time after Tsubasa Cat and before Karen Bee.

I don't know who the other girl is. There are many characters whose hairstyle has changed between the First Season and the Second Season of the light novel series, but they are not cut by Araragi:


Senjougahara Hitagi: She cut her hair short between the events of Karen Bee and Tsukihi Phoenix to break away from her past and start anew3.
Kanbaru Suruga: She initially kept her hair short in Suruga Monkey. However, after she was saved by Araragi, she started growing her hair3 up until the end of Hanamonogatari.
Hanekawa Tsubasa: After Tsubasa Tiger, her hair became black and white stripes like that of the white tiger she absorbed4. This is only a change in color, though.
Araragi Karen: In Tsukihi Phoenix, she nonchalantly cut off her own ponytail so that she could piggyback Araragi as a punishment game4. Araragi does not cut her hair himself. In the anime, she seems to grow her ponytail back a little in Hanamonogatari (episode 5).
Araragi Tsukihi: In the anime, story-wise chronologically, she had mid-back level hair in Nekomonogatari (Black) (episode 1), then bob cut hair in Nisemonogatari, then very long braided hair in Nekomonogatari (White), then straight waist-length hair in Hanamonogatari (episode 5). However, she is said to change her hairstyle very often3, so it is very unlikely that Araragi has anything to do with it.


1 Light novel - Nisemonogatari Volume 1 - Karen Bee Chapter 011. Anime - Nisemonogatari Episode 4
2 Published in Bakemonogatari Anime Complete Guidebook. According to Wikipedia.
3 Light novel - Nisemonogatari Volume 2 - Tsukihi Phoenix Chapter 005.
4 Light novel - Nekomongatari (White) - Tsubasa Tiger Chapter 066. Anime - Monogatari Series: Second Season Episode 5.
5 Light novel - Nisemonogatari Volume 2 - Tsukihi Phoenix Chapter 005. Anime - Nisemonogatari Episode 9.