<p>I recently had a problem with the z-axis of my printer. To resolve the issue with the Z axis not moving I remove the left polished rod. Am I able to use the printer with just one smooth rod?</p>

First a resounding no. Not a good idea. Are you saying it works now that you have removed the smooth rod?
That tells me for sure your issue was Binding. Which is a tricky problem to solve. Binding usually happens when your carriage is not level. Take a bubble leveler and verify.
Another time it happens is when your Acceleration / Jerk settings are too high. Try reducing the Acceleration for Z in the firmware.
Another possibility is your rod is Bent. Take the rod on a flat surface. Inspect it as you roll it around. Do the same with the other rod. If it bows and is not completely flat, then you will need to replace it.
Last is make sure your printers frame is put together. If it is causing the rod to bend as it is not aligned right then you should try to see if you can fix it and contact the seller.
Technically you can run without the second rod. Maybe. I do not advise. It is sort of like cutting off a leg because you have a cramp. It will hurt your overall quality and it is better to just resolve the issue.