Source: Tafsir al-Ahlam al-Kabir (Ibn Sirin)
The branch in a dream indicates children, brothers, and relatives. A green branch indicates a righteous son. A dry one indicates the death of a relative.
Source: Ta'tir al-Anam fi Ta'bir al-Manam (Al-Nabulsi)
The branch indicates a partner or a friend. Cutting it indicates separating from a partner or severing family ties.
Source: Al-Isharat fi Ilm al-Ibarat (Ibn Shahin)
The branch is interpreted as a son. Whoever sees himself breaking a branch is being undutiful to or harming his son.