In his first appearance, we learn that Armless Tiger Man was once a regular German guy working in a factory until he lost both his arms in an accident with a machine. Now he hates all machines with a burning passion, so the Nazis ship him over to America to fuck shit up as part of a plan to sabotage the war effort (and also as part of a plan to never see that guy again, because he creeps the Gestapo out). Once he's in the States, Armie finds the location of the factories he has to destroy and makes do with what he has, namely his feet:
In case you can't read German, he's saying, "FUCK! YOU! MACHINES!"
And his sharp, man-eating teeth (hence the "tiger" part):
Being the '40s, he was required to don a fedora and top coat before kicking a man to death.