Kasper comes from Celerina in the canton of Graubünden and graduated from the sports high school in Davos . Her father Curdin was once the trainer of the Swiss national cross-country skiing team and was responsible, among other things, for Andy Grünenfelder's successes . In contrast to him, his daughter Vanessa opted for alpine skiing. At the age of 15, Kasper took part in FIS races from November 2012 . At the European Youth Olympic Festival 2013 in Brașov , she finished fifth in the giant slalom. The first appearances in the European Cup followed in January 2014. In the same month she became Swiss giant slalom champion among the juniors. Two years after her European Cup debut, Kasper began to regularly finish in the points in the 2015/16 season. She achieved her best result at the Junior World Championships in March 2016 in Sochi , finishing 10th in the giant slalom.
On December 10, 2016, Kasper started a World Cup race for the first time , the giant slalom of Sestriere , where she was eliminated in the first run. After the rest of the season was rather average, she achieved a significant increase in performance in winter 2017/18. She won an FIS race for the first time and achieved her first podium in the European Cup on December 3, 2017. Five days later, on her 21st birthday, she won a European Cup giant slalom for the first time in Kvitfjell . She won her first World Cup points on December 29, 2017 when she finished 27th in the giant slalom in Lienz .