A dehydration experiment was carried out on Vitis vinifera L. cv Muscat of Alexandria (synonym Zibibbo) following the process for the production of renowned special dessert wines produced on Pantelleria island (Sicily, Italy). Harvested berries were pre-treated in a sodium hydroxide dipping solution (45 g/L, dipped for 185 s, 25 °C) to accelerate the drying process, rinsed, and dehydrated in simulated conditions (relative humidity 30%, 30 °C temperature, air speed 0.9 m/s). Three dehydration levels were achieved, corresponding to “Passolata”, “Bionda”, and “Malaga” stages (35%, 50%, and 65% of weight loss, respectively) of the Pantelleria denomination of origin (DOC). Grape skin mechanical properties, technological parameters, phenolics, and aroma profile varied considerably during dehydration. The most important aroma compounds for their olfactory impact, such as linalool, geraniol, nerol, and citronellol, especially in glycosylated forms, significantly increased in dried grapes compared to fresh ones, even if aroma profile modification occurred. A decrease in break skin force could have induced higher release of flavonoids. The findings showed relevant changes, allowing winemakers to better select the ratio of fresh and dehydrated grapes in the function of the final desired wine.