there is no simple way, but this workaround can work if you are going to paste into a clean track:
a] copy the needed area (for example: an entire track) to the new track regardless of how many instruments are contained in the source
b] in Advanced Edit, choose the correct selection mask (for example: “track in pattern” if you want to copy notes from an entire track)
c] in the “Instruments” section of the Advanced Edit select, one at a time, all the instruments which are present in the destination track and you don’t want to leave on it, then press “Delete”. this will delete from inside the selection mask (for example: the whole destination track) all the notes of the instrument selected as source for the Delete operation
edit: forget it, I didn’t notice that the different samples actually come from the same instrument, so my suggestion won’t work in your case
In the original instrument, set the volume of the snare sample to be silent.
In the duplicate copy, set the volume of the other samples (kick, highhats, etc) to be silent.
In the pattern editor, right-click on the drum track and choose “Duplicate track (incl. Patterns)”.
Position the cursor into the new duplicate track, then open the advanced editor view. Set the mode to “Track in Song”. In the “Instruments” section of advanced edit, set “Src. instr” to the original drum instrument, set “Dest. instr” to the duplicate copy of the drum instrument, and finally hit the “Swap” button.
Now you have one track playing the original drums minus the snare, and another track playing the original snare minus everything else.
Instead of simply muting the sounds, you could also replace them with a tiny portion (literally just a single sample point) of silence. Basically, do whatever it takes to prevent those notes from ever being heard, without actually deleting the sample completely.
Edit: Actually, I just tried it now. At first I thought you would have to keep some part of the sample there to keep the multi-sample instrument mapping in tact. But it looks like you can actually delete single multi-samples, and just leave the old mappings there, and Renoise is OK with that.