There are a lot of people, some even with a good deal of experience, who don't know this little tidbit about how the switches on microphones work. I had to work this out the hard way as a young sound guy with no internet. Years later I finally learned that just breaking the continuity isn't what shuts the mic off. It's actually something sort of counter intuitive.
On a balanced mic cable you have one conductor as a shield and two conductors carying the same signal but with opposite polarity. If you stick a switch anywhere in there that just breaks the signal, you're going to get a pop. If the phantom power is on you're going to get a really nasty pop. And if the phantom is on and you only break one conductor but not the other you're in danger of ruining a microphone.
Instead what you have to do is make those two conductors meet up. Identical signals of opposite polarity will cancel perfectly when summed. The beauty of this method is that because phantom power is delivered as +48 volts DC on each of those two conductors, they're both at the same voltage and therefore with respect to each other are at zero volts. Just let that last one go by you if you didn't get it. Phantom power is another lesson.
So how do you do this with a switch? Let me make the simplest possible diagram. I'm not even going to open MSPaint for this one, we're going old school ASCII art. (Just let that one go by too if you're too young to remember newsgroups.) On a double pole, double throw switch you've got six terminals that you can hook wires to. The two in the center of each side are usually the common, and the ones at either ends can be thought of as different outputs. When the switch is down, the center terminals are both connected to the bottom pins on that side (but kept separate, that's why it's called a double pole switch) and with the switch up the signal goes to the top pair of pins.
So how do you get those two separate but opposite signals to meet in the middle when you want the mic off (muted actually) and still keep them separate when you want it on? You only use two of the terminals on the same side of the switch. You don't even need to cut the wires from the diaphragm of the mic, just bare a little spot and solder each one to one side of the switch. When the switch is down, the signal doesn't pass through the switch at all, just passes right through the top two pins and on its way out to the mixer. Like this. The "C" is the contact off the switch. Technically wire two is electrically connected to the bottom terminal but since it's not connected to anything there's no issue.
| |--wire 2
| C |
When you want the mic muted, you move the switch up and the contact bridges the top two terminals and the two wires are shorted together. Normal and reversed polarity signals cancel each other out, phantom power remains balanced and your mic goes quiet.
| C |--wire1
| |--wire 2
There you have it Brethren of the Knob and Fader. Simple electronics at work for you on the gig.