There is a separate article about habitat fragmentation.
Fragmentation or Clonal Fragmentation is a form of asexual reproduction or cloning where an organism is split into fragments. The splitting may or may not be intentional. Each of these fragments develop into mature, fully grown individuals that are a clone of the original organism. If the organism is split any further the process is repeated.
Fragmentation is seen in many organisms such as molds, some annelid worms, and starfish. Binary fission of single-celled organisms such bacteria, protozoa and many algae is a type of fragmentation.
Molds, yeast, and mushrooms, all of which are part of the Fungi kingdom, produce tiny filaments called hyphae. These hyphae obtain food and nutrients from the body of other organisms to grow and fertilize. Then a piece of hyphae breaks off and grows into a new individual and the cycle continues.
Fragmentation is observed in nonvascular plants as well, liverworts and mosses.

Plants
Fragmentation is a very common type of vegetative reproduction in plants. Many trees, shrubs, nonwoody perennials, and ferns form clonal colonies by producing new rooted shoots, which increases the diameter of the colony. If a rooted shoot becomes detached from the colony, then fragmentation has occurred. There are several other mechanisms of natural fragmentation in plants.
People use fragmentation to artificially propagate many plants via division, layering, cuttings, grafting, micropropagation and storage organs, such as bulbs, corms, tubers and rhizomes.

A few plants produce adventitious plantlets on their leaves, which drop off and form independent plants, e.g. Tolmiea menziesii and Kalanchoe daigremontiana.
Some woody plants naturally shed twigs, termed cladoptosis, e.g. willow. The twigs may form roots in a suitable environment to establish a new plant.
River currents often tear off branch fragments from certain cottonwood species growing on riverbanks. Fragments reaching suitable environments can root and establish new plants.
Small pieces of moss "stems" or "leaves" are often scattered by wind, water or animals. If a moss fragment reaches a suitable environment, it can establish a new plant. [2]
Some cacti and other plants have jointed stems. When a stem segment, called a pad, falls off, it can root and form a new plant.
Leaves of some plants readily root when they fall off, e.g. Sedum and Echeveria.