Hi Jeong,
from you post it is very unclear to me what the problem is. The title says something with “SLink”, the text says something with mute… what is the problem?
Each input socket (on the rear of the SQ but also any connected socket or digital input) can be routed to many places.
An input channel where the mute does not completely mute the signal might mean you have the same input socket/source for that channel routed either to other input channels (which are not muted) or to a Mix External Input.
You can either check through the I/O screen Inputs section, or look through at the preamp section of all input channels on the processing screen, as well as all mix external inputs for mixes – both of which are in the same place at the top of each channel.
If this doesn’t answer the question, please explain what you are expecting to happen and what is actually happening.