OKAY HERES THE REAL DEAL, YES IT CAN BE SAFE IF DONE PROPERLY
NOTE Two of the big wires as you ask and the bare wire do indeed get you 120 volts IF YOU DO AS NOTED BELOW, i.e. two of the big need to be one Hot and one Neutral for 120 volts, as the two big hots line to line = 240 volts!!!!!!!!!!
1) Based on what you say, I am assuming the three big wires are two Hots (L1 & L2, 240 VAC, maybe a red and black) and a Neutral (a GrounDED conductor, maybe white) while the small bare wire is the safety Equipment GroundING conductor.
2) If thats the case, to get a 120 volt circuit for a 3 prong convenience outlet (or the stoves hard wired 120 VAC input), you would use one of the Hots,,,,,,,,The Neutral,,,,,,,,,The Equipment GroundING conductor)
3) It dont hurt to use bigger then necessary wire in THEORY, HOWEVER a 20 amp outlet and a 20 amp breaker are designed for more like 12 gauge wire ya know !!!! Therefore for a PRACTICAL consideration you might wanna consider use of a junction box etc. where you splice the bigger 6 Gauge wire down to the smaller 12 gauge which connects to your convenience outlet or your stove.
4) At the main panel you would install a 20 amp SINGLE POLE 120 volt breaker and feed your stove from it NOT the old DOUBLE POLE 240 volt breaker of course.
5) At the stove or convenience outlet the safety equipment GroundING conductor bonds to the case/frame metal ground or the safety Green grounding terminal on an outlet,,,,,,,,,,Hot (black) to the hot line terminal,,,,,,,Neutral (GrounDED conductor) to the white/Neutral terminal.
Runnin late for church so if I missed anyhting the other sparkies can add to or correct this hopefully
John T Long retired EE and rusty on this stuff dont ya know