One of the characteristic misunderstandings about evolution is usually under the argument of something like, "cats become dogs." I'm not saying that is what your argument is, but this is a common one that exemplifies a fundamental misunderstanding of the theory.
To properly assess what you mean by "a new creature evolving from another creature" you'd have to explain what you mean, precisely.
Because, for example, that numerous kinds of dog--what we refer to as "breeds"--are merely all variations within the subspecies Canis lupus familiaris. Since the domestic dog is a subspecies of wolf.
Speciation is specifically that phenomenon wherein changes in a population result in a new species; the working definition of a species has to do with fertile offspring resulting from a pairing. Horses and donkeys are separate species because even though they can successfully reproduce, the resulting offspring is infertile.
Speciation is said to occur when two populations descended from a common ancestor are no longer, when re-introduced, to produce fertile offspring.
While speciation is understood to usually takes many, many generations to happen, it has been observed in modern times, here is an example:
http://evolution.berkeley.edu/evolibrary/news/100201_speciation
Another phenomenon is the case of what are known as ring species, such as the Larus gulls,
https://en.wikipedia.org/wiki/Larus#Ring_species
Neighboring populations can interbreed, but one end of the "ring" and the other end of the "ring" cannot interbreed.
At this point, one might be tempted to say that we're still talking finches or gulls, etc. And that's fine, but the classification of organisms is a human construct--we're doing the classification, organisms don't classify themselves.
For example, we can say that coyotes and wolves are both canines. And that's accurate. But by the same token both canines and ursines are caniforms. The canine lineage and the bear lineage share a common ancestor, the same way that coyotes and wolves share a common ancestor. And that's really all there is to it.
The mechanism for changes in populations is natural selection, and this is readily acknowledged and observed even by those who reject evolution.
A cat will never produce a dog, but it's entirely possible for several populations of domesticated dog if they only breed among themselves, to over enough time be unable to breed with other populations of dogs, or wolves, and they would be regarded a new species. And this happening among populations of animals all over the world, over thousands--millions--of generations over the course of millions of years and this is precisely what we know of as evolution and its explanatory power in describing the diversity of life on earth. The only difference between what you describe as "variations of the same creature" and evolution is merely time and scale. Because given enough time variations of the same creature can result in two or more "new" creatures that share a common ancestor.
-CryptoLutheran