Upon buying Borderlands: The Game of the Year Edition, one of the things I noticed on the back of the back was a statement saying that part of the Secret Armory of General Knoxx DLC included having your level cap increased to level 61. However, I have beaten almost all areas of General Knoxx, except for some side-missions, and have yet to reach the level cap. What am I doing wrong? Is there a specific mission that will activate this or do I have to bust my butt killing enemies until I reach level 61 on my own?
According to this wiki page the cap increase seems to be 69 for the DLC, not 61 as you state in your question. With that aside...
Please let me know if I'm wrong, but it sounds like you're assuming that a 'level cap' is something that is 'awarded' to you.
A level cap is simply the limit to the highest level you can be. Just by having the General Knoxx DLC, your cap has been raised from 58 (assuming patch 1.4.1) to 69. This means you can now level up to 69, not that the cap level is awarded or activated by any event or mission.
So yes, you will have to keep killing enemies and/or do more missions (this may require you carrying over to a second playthrough if you run out of things to do.