After the attack on the steamboat, Marlow is gripped with the certainty that Kurtz is already dead. Since his entire mission is to find Kurtz and bring him back, this fills him with despair; his mission is hopeless and people have died for nothing. In frustration and fear, he throws his shoes -- filled with blood from a dying man -- overboard.
I was cut to the quick at the idea of having lost the inestimable privilege of listening to the gifted Kurtz. Of course I was wrong. The privilege was waiting for me. Oh, yes, I heard more than enough.
(Conrad, Heart of Darkness, eNotes eText)
It is here where part of Marlow's idealism is destroyed; he has spent too much of his personal time and effort keeping the mission on track. If Kurtz is dead, he has no reason to continue. It is only with hindsight that he realizes that he never should have wanted to meet Kurtz, and never should have allowed Kurtz to change him with words and deeds. The presence of Kurtz's brutality is more than Marlow's youthful idealism can handle, and it speaks more to his own persistence that he keeps traveling even though he is certain that Kurtz is dead.