The "Modern Synthesis", which is the foundation of modern biology, occurred during the 1930s and 1940s. It brought together Darwin's evolutionary mechanisms of selection (noting Darwin explicitly stated these were not the only mechanism), with Mendelian genetics and paleontology. Combining Mendelian genetics with Darwin's mechanisms took the work of Fisher and the like. These used statistical methods to show how gradual changes would occur. Paleontology by this stage, had discovered sufficient transitional forms to make evolution on these geological time scales accepted.
This synthesis provides the definition of evolution we use today. The term 'descent with modification' is more a description than a definition. I list a sample of these definitions here. The key points is that evolution is about genetic, inheritable changes in populations.
Non-inheritable changes (like amputations) are not evolution. Evolution does not mean a cat gives birth to a dog, or a monkey gives birth to a human. It operates at the level of populations.
Theodosius Dobzhansky (1937) Genetics and Origin of Species
Evolution is a change in gene frequencies through timeJohn Maynard Smith (1958) The Theory of Evolution
Evolution is merely a reflection of changed sequences of bases in nucleic acid moleculesDavid L Kirk (1980) Biology Today. 3rd ed.
a progressive, heritable change in gene frequencies in a population through succeeding generations, as a consequence of processes such as mutation, natural selection, and genetic driftHelena Curtis and N. Sue Barnes (1989), Biology, 5th ed.
In fact, evolution can be precisely defined as any change in the frequency of alleles within a gene pool from one generation to the next.