Source: The Great Interpretation of Dreams (Ibn Sirin)
Cutting the right hand in a dream indicates a false oath, theft, or abandoning prayer. Cutting the left indicates the death of a brother or sister or parting with a partner.
Source: Perfuming Humanity in the Expression of Dreams (Al-Nabulsi)
Cutting the hand indicates inability to earn or cutting family ties.
Source: Signs in the Science of Expressions (Ibn Shaheen)
Cutting the hand is interpreted as worry. Whoever sees his hand cut will be afflicted with worry.