Buzzing on computer speakers when LEDs are on
If this is the same project you described in this question(readers: "112 WS2811s in series" causing interference), your external speaker may not be filtered very well against energy radiated by nearby un-shielded wiring. Try a pair of headphones in place of the speaker - does it also buzz? If not, the speaker (system) is probably picking up the interference. If so, the pickup is probably within or near the Mac mini.

You could try a few simple solutions (or at least tests that might narrow the problem):


shielded audio cable from the Mac mini to the speaker;
shielding the speaker enclosure and grounding the shield;
shielding the connections to the LED string (obviously shielding the LED string itself is likely to be aesthetically undesirable);
separating the speaker from the LED strip by more distance; 
powering the mini from batteries - at least long enough to learn whether the power wiring might be involved.