|MadSci Network: Biochemistry|
The answer to your question (as posted, without any further assumptions) is that your assay results cannot be used to judge specific activity of mutant vs. native enzyme. The simplest reason why is that you are not working with pure enzyme - which means that the extract can contain completely different quantities of catalase depending on expression levels (mutant may not be folded 100% properly), age of culture, growth medium, etc. etc.
So, unless you have a highly accurate way to measure the concentration of your enzyme in the extract, you have no connection between activity and specific activity. Vmax won't help you because mutant and native enzyme may or may not have the same Vmax and other kinetic parameters. IMHO the only way to know for sure is to isolate both native and mutant enzymes and determine their specific activity under controlled conditions. The next best choice is to use e.g. Western blot (tightly controlled and at least 4-5 fold redundant experiments!) to estimate the concentration of catalase.
Try the links in the MadSci Library for more information on Biochemistry.