How should I know if my supervisor is deliberately ignoring my emails or he is simply bad in responding?
Your situation has the first thing I would try built in - ask your other adviser for help.  Your committee probably communicates with each other, even if they're in different departments at the same school.  Tell the adviser who is responding that you're held up because the other adviser hasn't replied, and see what they suggest.  If they are indeed in contact with them, then they might be able to nudge a reply.  They might also be able to inform you of anything going on that might be causing this, like an illness.

If that doesn't work, or if your responsive adviser is so far removed from the unresponsive one that they can't help, go to someone else in your department.  Do you have other junior committee members that might be able to help?  What about a grad student adviser?

The bottom line is that, while professors being bad at replying to emails is sadly common, it isn't professional, and you should keep at it.  With as much politeness and tact as possible, of course, since this person has a lot of power over your future here.