I know balistas, scorpions, and other war machines were used for sieges, but I'm wanting to know if they were ever used as offensive weapons for field battles. I've heard about the Battle of Jaxartes, but couldn't really find much information about the use of them in the battle. I would really appreciate any information you might have on the subject.
Several attempts to use artillery in the field are recorded but they were mostly unsuccessful, except when the artillery could be deployed in some protected place. For example, in the Battle of Jaxartes Alexander used catapults to clear the further bank of the river.
This article seems to be well-researched, and cites mostly contemporary sources.
There are carvings of wagon mounted "carroballista" (artillery) shown on Trajans Column in Rome. Trajans column is a commemoration of the Emperor Trajans conquest of Dacia and shows his Legions and their equipment carved in great detail. Being mounted in wagons would suggest the Carroballista were highly mobile and could be deployed in the field to fire missiles at the enemy.
Romans didn't even use archers that much. They relied heavily on their very well trained infantry; and history shows that they could adapt to nearly any situation effectively. Any other troop types were auxilia kept for situational backup. It wasn't until the late period that other troops dominated the field. Artillery is slow and vulnerable to attack. A battlefield is always moving around and it takes specialised skill and calculation to use artillery. So, it's letting fly at a charging enemy long distance with wind and poor accuracy at play, recalculating every shot as they move; or firing over your allies heads, in which case you need high ground without obscurities or a vulnerable flank position.
The Romans of course had a highly trained standing army with specialised units. Medieval armies were not so, other than later mercenaries. But the same issues applied.
Therefore, artillery was best used in siege warfare, against a large,still target. It was impractical elsewhere and mainly a tool of intimidation and a show of power in the field.