We know that the sword is the Word of God. The writer of Hebrews said For the word of God is living and powerful, and sharper than any two-edged sword, piercing even to the division of soul and spirit, and of joints and marrow, and is a discerner of the thoughts and intents of the heart (Hebrews 4:12). Also, Ephesians 6:17 encourages us to take the helmet of salvation, and the sword of the Spirit, which is the word of God.
If you study the history of the two-edged sword, you will find that it was developed and mastered by the Romans. As a matter of fact, it is credited with the rapid rise of the Roman Empire. While other nations were still using a single-edged sword that could only cut one way, the Romans had mastered the double edged sword that could cut two ways. This gave them a huge advantage on the battle field. It made the Roman Centurion lethal. It would be the equivalent of a single-shot firearm as compared to an automatic. The later will do much more damage, much more quickly.
The two edges can also represent the Truth and the Severity of the Word of God. If it is allowed to cut one way, Truth can be like a surgical scalpel that the Master Physician uses to repair, heal, remove, and restore our lives. However, if it is allowed to cut the other way, Severity can be an instrument of judgment against those who choose to not repent after having been exposed to the Truth.