The quality of coins varied significantly from mint to mint. In general a blank would be cast first. These would come out more or less perfectly round; depending on your definition of perfectly round. No one was casting to modern tolerances. Depending on mint, these might then be worked to trim away sprue and flashing. In any case though these blanks were a consistent size and weight.

This round blank was then placed on a die, an obverse die and punch were placed above it. Then the punch would be hammered on a couple times to “strike” the dies into the blank.

This is where the first inconsistency creeps in. There was no method for ensuring that different coins were struck in the same place. The stamped images were as often than not off center; resulting, as you note, in more material on one side or another. And the act of striking could make the coins a bit bulgy and the edges were unevenly squished. This wasn’t considered a major issue though. Because the blanks had been cast prior to striking, the coins were still consistently a single size and weight, even though they looked lopsided.

Once out of the mint the second inconsistency starts to happen. Metal is valuable. So folks would shave their coins. They’d cut small slivers off the edges; as much as they’d think they could get away with. The previously round (more or less with some squished edges) coins pretty quickly start to look less round, and increasingly more like the coins in your picture.

In good times coins were monitored and pulled when they got too clipped. And it wasn’t at all uncommon for coins to be weighed in the market. The Denarius was a consistent weight, 1/72 a roman pound (4.5g). So if coins were looking too bad merchants often would demand a pile of coins be weighed rather than counted.

To get to your question through, there really wasn’t any “excess” material. The use of precast blanks meant the weight of material remained consistent from coin to coin, even if they didn’t look exactly the same.