When removing a reactant and equilibrium shifts left, doesn't this make an excess of the 2nd reactant, forcing equilibrium back to the right?
The thing to be careful about with Le Chatelier's principle is that it relates to equilibria :


  Le Châtelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change to reestablish an equilibrium. 


Le Châtelier's Principle

Now when you say in the above "But when the reaction shifts to the left, isn't a side effect  ..." note you can't use Le Chatelier's principle here again so fast because the system has not reached an equilibrium yet, it is just moving towards one.

It is likely that the next thing you will study is how to actually calculate the new equilibrium conditions. This gives usually a deeper understanding of how changes in various conditions make the reaction move forward/backward establishing new equilibrium conditions.