Final answer:
The correct word to use is 'mince,' which can describe walking or speaking in an exaggeratedly delicate manner, or the act of chopping food into tiny pieces.
Step-by-step explanation:
The word you're looking for to complete the sentence "To ______________________ means to walk or speak affectedly; might also mean to chop into very small pieces" is mince. This verb can indeed refer to both walking or speaking in an affectedly dainty way, as well as to cutting or grinding food into very small pieces. In contrast to the other options, malicious pertains to a desire to harm someone, managerial relates to management or managers, and mandatory means required by law or rules.