Break a circuit on a alarm clock

Ok, so what I understand from your question you need the following to make a basic alarm clock:

  1. Any RTC Module like the DS3231/DS1307
  2. 4 digit 7-Segment Display for showing the time
  3. Arduino, but I would recommend using the NODEMCU ESP8266 so that you can set the time using app in your mobile.
  4. One Buzzer/ low wattage speaker

To disable the clock, you can use a push-button, so that when the value of the push button goes high (pressed) the buzzer stops. This can be done through a while loop maybe.

You can also do the above with a app, so that when you click a button in the app the buzzer goes off.

Regarding @daveve's answer you need a opto-isolated relay like this:

Regards.