Yes - the common California tide pool sea anemonae can be 3" by 5" and reproduces asexually. There are also some frogs that reproduce asexually that are above that size threshold.

Some whip tail lizards, from the Cnemidophorus family, in the U.S. Southwest, Mexico, and South America reproduce asexually. They are all females that reproduce by parthenogenesis (the female lays eggs that are unfertilized and develop into female lizards). They are definitely longer than 2".

First let me give you a definition: Asexual reproduction is reproduction where the genetic material comes from one individual.

I have summarized for you a web-site that talks about asexual reproduction:
asexual reproduction.

There are several different ways to reproduce asexually:

1. Splitting
This involves the parent organism dividing into two new offspring by splitting. For this to happen the DNA multiplies, dividing into two equal halves, then the cell divides. Many one- celled animals undergo this.
2. Budding
Involves the growth and separation of a small part of a parent to form a new organism. When animals/fungi do this it is called Budding. Animals that undergo budding are: hydra, sea anemones, fungi. When plants do it, it is called vegetative propagation.
3. Fragmenting
This involves a form of repair to damaged or broken parts of organisms called fragmentation - when a small piece breaks off and forms an entirely new organism. Organisms that undergo this are sponge, planarian, starfish, black worms. Regeneration is when there is a replacement or a re-growth of missing parts. Organisms that undergo this are starfish for example.
4. Spores and Parthenogenesis
Spores are packages of DNA with a little cytoplasm surrounded by a tough (protective)outer wall. Parthenogenesis is when unfertilized egg develops into an adult. For example an unfertilized bee egg develops into a male drone. Fertilized eggs develop into female worker bees.

I was a bit surprised by your question, since I don't usually think of plants as reproducing asexually, but it is true that they can do this. Algae (not considered true plants) can also reproduce asexually, by fragmentation, and do it quite well (this is one of the reasons algae are able to overgrow coral reefs and kill them).

So, to answer your question, yes! A starfish is an example of a largish animal that can reproduce asexually. If a leg gets cut off of the main body (central disc), as long as there is a small piece of the main body still attached to the leg, you will get two starfish eventually. Same if you cut them in half. Some starfish can get quite large (12 inches in diameter or more). Sea anemones can also do this. As long as the pieces of the original anemone contain a piece of the basal disk (the trunk of the anemone), they will all grow into new, whole anemones.

If you've ever been lucky enough to see a flatworm while in the ocean, you know they can get really large. If you cut a flatworm in the right spot, you will get two new flatworms, both with heads and tails. This type of asexual reproduction is called "regeneration". Sponges produce little spores, almost, called gemmules that are considered asexual reproduction because the offspring are genetically identical to the parent. Sponges can be quite large. If you've ever been diving in the Caribbean or the Indo-Pacific (e.g. Australia, Papua New Guinea) there are some vase sponges that are so large, a diver can swim inside the opening.

So there are some examples of large animals that can reproduce asexually. Many, many examples are from aquatic animals. I don't really know why this is. Maybe you can think of a reason.