Rarely, if ever true. Their win/loss record is pretty average for most of Rome's history, nowhere near a case of "sending another legion to be killed". The majority of battles which were lost ended up with them running away or falling back to a nearby fortified field camp, often covered by a small number of die-hard Triarii or other aging veterans who were willing to sacrifice themselves to save the rest of the army. Some routers were likely run down by cavalry or pursued to exhaustion by the victorious infantry, but far from all. In most other cases aside from Rome in that timeframe, a defeated army would take years to replace the weapons and armor (especially time consuming items such as chain mail), even if the manpower were available to reform the army. In Rome's case, they were able to rebound quickly, recruiting, rearming, and fielding fresh army after army (often from the remnants of the last one). It wasn't just a matter of throwing warm bodies at the enemy, it was a robust economic system and a faith in the city itself that allowed for recovery even in the most dire situations. Even the one army "totally destroyed" by Hannibal had survivors, and many of the men who were captured were released after being humiliated and beaten ("running the gauntlet"), but returned to Rome minus equipment.
They were not even remotely close to being the "Red Army" of their day: Egypt might have been closer to that, with minimally armored and lightly armed troops fielded in volume, but even they eventually formed an "imitation Legion" of better-equipped troops. Rome had both the production capacity and the manpower to replace losses, and mostly decent quality troops, but the leadership was too frequently based on political favors and voter popularity, not on merit.
