To specifically answer the question: Adamantium CAN cut through vibranium. Adamantium is an order of magnitude more indestructible than vibranium. But there are extenuating circumstances.
Vibranium is an extraterrestrial metal of unknown origin. There are two types of vibranium:
Wakandan vibranium, which absorbs vibration and dispels kinetic energy
Antartic vibranium which disrupts metallic structures, including adamantium and is known by another name: anti-metal
The picture depicts Captain America's shield versus Wolverine's claws. Cap's shield is proto-adamantium and Wolverine's claws are made of only beta admantinium. (Wolverine was initially created with True Adamantium, but after interacting with his healing factor the metal degraded to beta Adamantium.)
Captain America shield is not made only of Wakandan vibranium, despite what the movie might have mentioned. On Marvel Earth #616, his shield is an alloy of proto-adamantium, a unique and never again duplicated mixture of adamantium and vibranium, making it even stronger than pure adamantium and giving it special properties neither metal seems to possess.
In the most recent storylines of the Avengers comics, his shield was broken and repaired by Asgardian smiths who added a bit of uru metal to the mixture, thus making it even more unique with a potential to be enchanted.
Thus in this circumstance, Cap's shield is stronger than Wolverine's claws.