The Beam Gun is a large weapon with four blue crystals and one in the center of it. Based on its name, it would fire a beam. However, the coding is incomplete, as it doesn't mention the projectile the Beam Gun was supposed to fire. The model itself has a screen with numbers on it, which was removed from every other weapon in the game before release. This suggests that the model wasn't worked on after they changed the weapon's displays to either be broken or display junk. There are a few projectiles which sound like they might've been used for the Beam Gun, but since it's coding doesn't list a projectile, it is impossible to determine what projectile code it might've used. The ammunition type it would use is unknown, but it might've used Plasma based on the gun's visual similarity with the XL 808 Plasma Rifle.
Based on this information, it seems that the Beam Gun was quite incomplete when it was cut. The beam fired by the Beam Gun was either a placeholder or replaced by another another model, the coding is incomplete, and the model still needed a minor update to match the final's weapons.
Interestingly enough, the HUD icon for the Beam Gun has different colors, suggesting it was made earlier than the final's textures were made.
The weapon was removed from the game, but the model, HUD icon, and coding are still in the game's files.
The Beam Gun looks and purpose is the same as in 2 other weapons: the scrapped weapon from Serious Sam: The First Encounter's first public beta Test 1 Ghost Buster, and a weapon from Serious Sam: Next Encounter called the Sirian Power Gun.