Can I remove one spring from my suspension fork?
No, i would not advise doing so. If it is a dual spring fork like your image illustrates one spring-less leg would put the entire thing under constant stress. This seems like a horrible idea all around. It may loosen up some after time, and you may be able to adjust some settings if that is the same fork in the image. 

Does is have any knobs on the top of the legs like those in the image?

I would advise either buying softer springs if available, a new fork, or just learning to deal with it. Inexpensive fork are not really made to be adjusted or tampered with generally and i would not trust them to perform after doing so.