Concerned about 3 circuits interconnected in 1 box
You're not supposed to disconnect wires with the power on. However, this can be a real problem in a promiscuous-neutral situation, where you don't realize another circuit is borrowing this circuit's neutral, thus putting current on it.  It won't even show up with a voltage tester until you disconnect the neutral, and then whammo.  

Don't let your guard down around neutral (or any other wire that's "supposed" to be safe); this is a good example of why. 

White wires normally handle current

Current flows in loops. That's why everything has at least 2 wires. Current is flowing out the hot wire, to the appliances, then returning on the neutral wire.  If you disconnect neutral, it'll spark because you are interrupting current. 

Further, the disconnected side of the neutral will measure out as "hot", because electricity is trying to flow from hot via the appliance back to neutral, but it can't get back.  It's normal in this case to read mains voltage across the neutral gap. (in fact, this "lighting up" of neutral is a huge reason ground is separate!) 

Absolutely NO promiscuous neutrals

Your box's current wiring has neutrals sleeping with everybody.  That's quick and lazy wiring, but it's very bad.  Imagine you run three 20A circuits, that just happened to return all their current on the same neutral. That neutral will flow how much power? Anyone, anyone, Bueller? 60 amps, that is correct.  Neutral wires don't have circuit breakers, so that's a huge problem.  The neutral will set the house on fire and the breaker will never know.  

There are ways to exploit split-phase or 3-phase geometry to intentionally share neutral wires (so that neutral handles only differential current), but you don't appear to be doing it here. 

Currents must be equal in every cable or conduit

This is another rule that outlaws the promiscuous neutral.  AC power kicks a heck of an electromagnetic field (EMF).  When two adjacent wires have opposite flow, their EMFs cancel each other out.  That's vital for safety - EMF causes eddy current heating, which starts fires, and vibration (which cracks copper and causes arc fires). 

Imagine many ants running up and down branches of a tree. They never leap from branch to branch; they'll come down branch 1 and go up branch 2 rather than jumping.  At the end of the day all ants go home.  If you put ant turnstiles anywhere on the tree, you'd have exactly the same number of ants going out as coming back.  Mains electrical is like that -- if you wire all your cables in tree/branch topology with each branch being 1 cable, currents will inherently be equal in all cables. 

See how current is not equal in that 10-8-12 sequence.  Current goes out the orange hot, but comes back on the red neutral via a different cable. 

So... where hot goes, neutral follows. Always.

Now, with all that in mind, look at your drawing. Its hot (purple) serves two downline cables (OK so far) -- but it's neutral (red) serves two completely different downline cables (no, no, no!) 

So pick and choose.  For instance have green neutral go straight across to that cable orange hot serves.   Then have red neutral serve the same cables that purple hot serves.    This is mandatory and you should do it immediately. 

When you have two disparate circuits in the same box, it's preferred to partition them.  Or at least mark them with colored tape -- white and gray are allowable colors for neutral. 

This may not solve all your problems, but at least this will be correct.  

And to review: Hook up wires in order, and push them into the back of the box in order:  


Safety Grounds (green, green-yellow and bare) first.  They go in the back, you're unlikely to need to disturb them later, and this heads off a common problem where a device has a ground fault. If you hook up ground last, then it seems like ground is the problem when actually the device is defective.  Hook grounds first.    By the way, grounds are promiscuous - hook them all together along with pigtails to the steel box and to any devices which mount there.  
Then Neutrals (white or gray)-- keeping diligent separation.  I recommend marking, but use only white or gray, but don't go past middle gray, or it'll be confused as black on a switch loop.  
Hots (every other color) on top.