Theory:

Plants can also be grown through other methods of reproduction other than sexual reproduction.
 
Plants can be developed (or propagated) through the cuttings of
  • stem,
  • roots and
  • leaves.
stem cutting.jpg
 
The above picture shows a plant developed through stem cutting.
This type of reproduction are called asexual reproduction as it does not involve the sexual parts of plants like stamen or pistil.
 
This is also called vegetative propagation as the vegetative parts of the plants are used for the reproduction.

Reproduction through budding and spore:
 
Mushrooms especially Yeasts reproduce through budding. Budding is a process in which the matured yeast grow a structure called bud (also called daughter cell). Once the bud grows well it detaches itself from the parent yeast and starts living as a separate entity. This is also a type of vegetative propagation.

Unlike budding, the macroscopic mushrooms, some algae, moss and ferns propagate through spores developed in special structures. These spores will develop in to a new plant in favourable conditions growth.
 
mushroom-1374048_1280.jpg
 
In spirogyra a filamentous algae on maturity split into multiple filaments and each filament become a baby algae. This is known as fragmentation.
 
Summary of vegetative propagation with examples:
 
Vegetative propagation
Example
Stem cuttingsSugarcane, rose, grapes, jasmine
Leaf cuttingsBryophyllum
Root cuttingsSweet potato, blackberry
SporesMushrooms
Reference:
Image credit:
Stem cutting: Free image from Wikimedia : https://upload.wikimedia.org/wikipedia/commons/thumb/c/c6/Stem_Cutting.jpg/1280px-Stem_Cutting.jpg
Mushroom: Free image by skeeze from Pixabay ; https://pixabay.com/photos/mushroom-wild-fungi-nature-1374048/