Sympathetic buzzing eh.
Don't use any tissue paper inbetween snare wires and snare reso head or the cloth trick as mentioned above.
Just take some time out to tune your snare properly, but you have to understand that no matter what, as long as your snare is tuned to a similar frequency as another source of sound, there will be sympathetic vibrations.
You can try retuning both sides of the head to see if you can get rid of most of the buzzing. If not, then loosen the tuning lugs at both sides where you have the snare bed. Then tighten the other lugs to compensate for the tension.
But also, since you mention "a tom", I assume it's only one offending tom that is making your snare drum go crazy eh? If that's the case, I would suggest you to tune up or tune down that specific tom.