I don't know what the DR uses for a clutch mechanism, presumably someone here does, but first are you SURE the clutch is correctly adjusted? There are TWO adjustments - one at the lever, where there should be about 1/8th inch FREE play at the lever where it touches the mount bracket, before the cable tightens. That equals around a half inch at the lever end.
Second, there is an adjustment at the bottom end of the cable. It will be on the cable and visible, or on most Suzukis, inside a cover or rubber plug near the end of the cable. If you can find it, you may see a screw and locknut. When you pull on the clutch cable the screw and locknut rotate and move in a little. IF SO - loosen the locknut and back the screw OUT - it should be very free. Make SURE the cable adjuster at the top has LOTS of free play. Give it some more. THEN screw the screw in until it just lightly stops. Back it out 1/4 turn, and tighten the locknut, making sure the screw doesn't move in as you tighten the nut. Then readjust the cable.
If the clutch still slips, it's toast. You can take it apart and possibly sand the metal plates lightly, and the ocrk plates, but this is dangerous - you can get sand embedded in the plates, which either scores and wears the plates or gets loose and damages the engine. Replacement is recommended.
As noted earlier, get a full set of spares - that includes all cables, levers

(as you've already discovered,) a gasket set (you'll need the clutch cover gasket if you take it apart), brake pads/shoes, and whatever else a Suzuki dealer recommends for that model.
For correct terminology see
our Tech glossary
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Grant Johnson
Seek, and ye shall find.
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One world, Two wheels.
www.HorizonsUnlimited.com