Your installation of Redneck Rampage should have come with a tool called KEXTRACT.EXE. (Whether or not it comes with the GoG version I honestly can't remember, as it's been a while since I installed it, and if it was missing I would have copied from another BUILD engine game I already had installed.)
If you have an actual CD-ROM of the game, you might find KEXTRACT.EXE under [disc_drive]:\GOODIES.
Start DOSbox and go to the game's location. At very least, make sure you have KEXTRACT.EXE and REDNECK.GRP in the same directory. (I can't remember if DOS4GW.EXE is required, but that should come with the game, too.)
You can extract the files into the game directory, or to keep things tidy, dump them to a subdirectory:
MKDIR TEMP
Switch to the new directory:
CD TEMP
To extract just the voices, type
..\KEXTRACT.EXE ..\REDNECK.GRP *.VOC
If you want to extract
everything, type
..\KEXTRACT.EXE ..\REDNECK.GRP *.*
If you need a sound editor, I would recommend GoldWave.