The announcer in Modern Warfare can be very annoying at times, so it's no wonder that people really want to mute him. Luckily for us, it's very easy to mute him, and it's even possible from the main menu. However, it can be a bit tricky to locate exactly where to do it.
What you need to do to mute the announcer is to head to the main menu and choose the Audio options. Find the option to change the dialogue volume and turn this all the way to 0. This will effectively mute the announcer.
If you want to know what he announces without hearing the annoying voice, you can turn on subtitles to get the announcements there.
Just a little warning though: this will mute all dialogue in the game, including enemies and friends, so you will play at a disadvantage.