In the case of seedless grapes, a cutting is taken from the vine and planted. These days horticulturists use rooting hormones to quicken the process.
Grape vines just wither when the conditions are unfavourable. In places where they are grown, they continue to survive around the year. It would take too much time for a sapling to grow big enough to give fruit.
"A love affair with knowledge will never end in heartbreak." -Michael Garrett Marino
The biological occurrence known as "STENOSPERMOCARPY" is what causes the berries of grape vines to be seedless. More accurately, this is a mechanism in the plant that generates underdeveloped seeds, or tiny seeds that are barely visible, within the fruit.
And surprisingly, the absence of seeds does not affect the reproduction because, like other species of trees or plants, it reproduces through cuttings & grafting as well.
If we try to give one scientific explanation then, new plants can also be made from existing plants wherein the adult grape plant stems are sliced diagonally and cut into sections. The cut ends are then dipped into a rooting hormone and planted. The new plants that begin to grow are basically genetic clones of the original parent plant. The scientists can grow plant of different other fruits or species in this way.
Even this myself did during school days for one of the science projects. Although not successful that time but at least have contributed for the above briefings.
The common courtyard Jasmine is also grown and cultivated like that. Many vegetables, tubers and flowering plants are planted and grown like that. For Tapioca or Sugarcane, it is the stem that is used for further planting.In the vines one common example is the betel vine and pepper. For certain crops just when the harvest is nearing a separate arrangement is made to grow the next crop by growing the cut stems or cut creeper vine.