The only evidence that creationists have is the bible. Scientists have carbon dating, examination of sediment levels and fossils, breeding of animals to enforce specific traits (most notably dogs), genetic similarities, and the effects of genetic mutations. .
Lets discuss this 'evidence' of evolution that you have brought up. Two seperate points actually, one genetic mutation;
a mutation of a gene will not break through the barrier of species or kind. Mutation because they are destructive, damaging or completely destructive, a mutation is the destruction of genetic information, not a single mutated gene has ever been found to be beneficial to a species, as one Nobel Prize winning scientist stated "There are no genetic process that science knows of that could produce the changes required for the process of evolution." Genetic mutations have never been observed to improve, modify or make an organism more complex or efficient, not one convincing case exists. Mutations are abnormalites due to the destruction of genetic code, they are always detrimental to the species concerned. This completely exterminates any belief that evolution has happened via genetic mutation.
Dog breeding; for beginners is a very poor example of evolution, for the simple reason that an intelligent human is required to crossbreed dogs, one can hardly cite this as an example of 'unsupervised, random, impersonal, unpredictable, natural processes'. Futhermore dog breeders only produce variations within a given species, so selective breeding is not an example of natural selection, but it is an example of intelligent design. Variation does not constitute evidence for evolution because variations are the outcomes of different combinations of already existing genetic code, they do not add any new characteristic to the genetic information. Any variation in the gene pool of a species or sub-species when left alone to nature without specific human intelligence guidence will simply revert to type, the variation within the species, whether broad i.e. dogs or very small i.e. cheetahs is due to species spercific gene pool genetic code variation, no new code is created and neither can the code cross species DNA barrier.