Is it normal for disk activity to disturb MySQL performance?
From my experience, it is better to separate the MySQL data files and log files from other application files. When you don't have dedicated MySQL server, separate the data files and log files to different disks. I have faced the similar issue and we resolved by changing our data directory and log files to a each dedicated separate directories. I suggest you to go through the MOCA (MySQL optimal configuration architecture) for better understanding. I hope this will help you. 

Thanks.