I currently have a 1 minute long video where in the beginning of the video someone says something inappropriate. I was wondering what the easiest way to silence that part of the video would be. I am wondering if Quicktime or iMovie can do the job in Mac.
You'll probably need a Non Linear editing tool such as the one you mentioned (iMovie) to achieve this, as you'd need the ability to separate your audio from video.
See How to separate audio from a video track in iMovie to guide you using iMovie.