Yes, 1045 carbon steel is capable of cutting. It is a commonly used steel in various applications, including knife making and sword production. 1045 steel is a medium-carbon steel with a carbon content of around 0.45%, which provides a good balance of hardness, toughness, and ease of processing.

While 1045 steel is not as hard as higher carbon steels like 1095 or some tool steels, it can still achieve a sufficient level of hardness through proper heat treatment. With the appropriate heat treatment process, 1045 steel can be hardened to a degree that allows it to hold a sharp edge and cut effectively.

It's worth noting that the cutting performance of a blade made from 1045 carbon steel can be influenced by various factors, including the blade geometry, edge geometry, heat treatment quality, and the skill of the blade's user. Proper sharpening techniques and maintenance practices also play a significant role in maintaining the blade's cutting ability.

While 1045 steel can be suitable for cutting tasks, it is important to consider the specific requirements and intended use of the blade. For specialized cutting applications or demanding cutting tasks, higher carbon steels with enhanced hardness and edge retention may be more appropriate.