A gruesome obstacle lay in the middle of the road, halting the advancing army. Only by clearing this tragic sight from the path could the warriors resume their crucial pursuit. The primary approach among commentators is that the body had to be physically dragged off the road to allow the troops to pass. Specifically, [רש"י] notes that the corpse was pulled aside in the same way one removes impurities from silver. Removing the body prevented any further delay. As [מלבי"ם] emphasizes, the very moment the path was clear, all the men immediately surged forward to follow Joab without hesitation.
Looking at the broader context of this assassination, [אברבנאל] explores why Joab committed this murder in the first place. Joab was driven by deep jealousy. He knew King David was still angry with him for killing Absalom, and he was aware of the king's plan to replace him by appointing Amasa as the new commander of the army. To justify his violent act, Joab claimed that Amasa was effectively a rebel against the crown because he had failed to arrive by the deadline the king had set for him.
Following the murder, King David's silence was deafening. Unlike his public mourning and cursing after the earlier murder of Abner, David neither cursed Joab nor mourned Amasa. [אברבנאל] explains that this silence stemmed from two main factors. First, David was highly anxious about the ongoing rebellion of Sheba son of Bichri. He feared that if he confronted Joab, the powerful commander might defect and join the rebel forces. Second, because Joab was also the one who had killed Absalom, David could not publicly display a heavier grief for Amasa than he had shown for his own son.