You must be query number 20 on that problem this month!
Your scooter is suffering from a classic case of clutch shudder, and it's NOT a serious problem. Either there is a bad build-up of dust from wear of the clutch pads inside the clutch bell, or the pads and bell have become glazed, or both.
Sometimes, simply blowing the dust out will solve the problem (temporarily, as it always comes back eventually). Pry off the round chrome clutch cover with the Vespa logo, and you will see some small elongated holes. The clutch bell is immediately behind those holes, and it has larger holes. Using a blowgun attachment on an air compressor, aim the airstream into the holes in a variety of directions while slowly rotating the rear wheel in an attempt to reach as much of the clutch assembly as possible. Best to wear a dust mask or hold your breath through the entire procedure, as a considerable amount of fine, black dust will likely emanate.
Some folks prefer to use aerosol brake cleaner for this task, but I'm personally wary of using the powerful brake cleaner solvent where it might get onto the clutch shaft oil seals. If you do use brake cleaner, be especially careful not to breath the fumes.
If blowing out the dust doesn't solve the problem, then your clutch pads and bell are likely glazed. Unfortunately, the only way to deal with that is to remove the entire transmission cover. Once the tranny cover is off, you can simply slide the clutch bell off and sand the faces of the clutch pads and the inside surface of the bell lightly with 220-grit sandpaper.
This problem is endemic with many CVT scooters, however -- in my experience -- it seems to be aggravated by riders who are too timid in their take-off from a stop. Not giving the engine sufficient throttle allows the barely engaged clutch to slip a little, creating more wear, dust, and glazing from heat.
Ride it like you stole it!