Mono-oxidized and dioxidized tryptophan
First, you can use Google Ngram viewer to check out how often and in which context proposed words and their combination is used/has been used in the literature. 

Second, I feel that "mono-oxidized" is overly redundant and just "oxidized" will deliver. Even in Russian you would rarely say so ("моноокисленный" or "единожды окисленный" is usually seen as an unnecessary complication in most cases). For "dioxidized" there are plenty examples when it is used in a similar context both in inorganic and bio chemistry, so it should a safe usage from what I see.

There is also an another option to say "two-stage oxidation" ("окисленный по двум ступеням") instead of "dioxidized" if you want to underline that the process has been carried out step by step.