There could be a few reasons, and without experimenting it may be difficult to know for certain.
Is the wet food a new variety? The cat may just be unsure of the food, giving it a "taste test" before deciding to finish it. I've seen my cats do similar things with new foods.
Another possibility is a cat's natural instinctive behavior pattern: "hunt, play, eat, clean, sleep". If you watch a cat hunt live prey, you'll notice it won't eat its prey immediately when she catches it. Instead, it will play with it before finally eating, cleaning itself, and then resting for the next hunt. I would recommend playing with your cat before feeding, allowing it to get the "hunt & play" urges out before meals and then immediately follow play sessions with food.
It's also possible that your cat doesn't feel "secure" in the space where the food bowl is kept and is taking the food elsewhere to enjoy it.
- Are there other cats in the house?
- Have there ever been cats in the house before that might have left "territorial markings" (urine, can be checked with a black light) in that spot?
- Is it near a window where neighborhood cats may be seen from?
Try moving the food bowl, or playing and giving treats to her around the food bowl so she associates "good things" with that spot. Depending on how dependent your cat is on you, she may just want your presence while eating. My cats prefer to eat when I'm close by and will rarely finish their meals without me around.
Maybe the cat isn't happy with the taste of the wet food? Have you tried other varieties? Some cats are very picky and will take their time if they don't like it as much.
And of course, it also could just be your cat's individual personality and instincts. I'd advise putting a plastic matt near the food bowl to make cleanup easier.