Mechanistically is the adverb that belongs with mechanistic. You use it when someone explains or treats things as if they were machines. “He described the brain mechanistically” means he talked about it as a system of parts that push other parts, not as a place of feelings or soul. Same classroom and philosophy flavour: you will not hear it in a night market. It can sound slightly critical, as if the speaker thinks that machine picture is too simple — though actually some scientists wear the word proudly. They want a mechanistically clear account, with every step spelled out, the way you would explain an engine.