How to disable a game component (audio)

Note that you can also just simply call AudioSource.mute through the button:

If you just want to toggle mute, make a small script that does exactly that:

 using UnityEngine;
 
 [RequireComponent(typeof(AudioSource))]
 public class AudioSourceMuteToggler : MonoBehaviour
 {
     public void ToggleMute()
     {
         var a = GetComponent<AudioSource>();
         a.mute = !a.mute;
     }
 }

If you want explicit control over Play(), a simple skeleton class could be this:

 using UnityEngine;
 
 [RequireComponent(typeof(AudioSource))]
 public class MuteableAudio : MonoBehaviour
 {
     bool isMuted;
 
     public void Mute()
     {
         isMuted = true;
         GetComponent<AudioSource>().Stop();
     }
 
     public void Unmute()
     {
         isMuted = false;
     }
 
     public void Play()
     {
         if (!isMuted)
             GetComponent<AudioSource>().Play();
     }
 }

Then you can call Mute, Unmute or Play on this script instead of AudioSource. If you want to control multiple audio sources with the same script, make the boolean static. If you want more fine grained control over audio groups, consider using AudioMixers with exposed parameters (SetFloat) for Attenuation/Volume.

You can also disable the AudioSource component instead of explicity controlling a boolean variable but that will give you warnings when you call Play, and I am not a big fan of warnings. It's up to your preference.