Is it possible that a complex humanoid creature to somehow still use Mitosis as a method for reproduction, and if so, what would it look like?
While BlindKungFuMaster is sort of correct, I don't think that is what you had in mind.
You want a humanoid body that splits in half, and then the resulting two forms are viable individuals.
The problem with this is that splitting a human in half makes us non-functional, so first you need to duplicate all the vital organs. But that's still not enough, how do you do the split? The most likely way would be a vertical split from the top of the head to the crotch, this has the least "surface area" to create and reseal.
So this would probably start with the growth of vestigial limbs at the front and back of the body, these would grow gradually, becoming more and more viable. At the same time internally the vital organs are duplicating and splitting, until eventually you have two hearts, the two lobes of the lung have separated and are starting to form a new pair.
The head would start to expand outwards and new brain cells fill in as memories are copied between the two halves as they gradually become more and more separate.
After a few months you have a body with two heads, and extra limbs front and back. The two systems would continue to separate and new skin grow in to cover them all until eventually they fall completely apart and rise as two separate individuals. They then have to argue over who gets which possessions.
During early stages they would be able to function as normal. Once the separation grew advanced enough this would become harder and the last few weeks would involve bed rest most likely. The splitting and reforming of the brain would most likely cause confusion and mood swings, and the two resulting people while being genetically identical would not have fully identical memories or personalities.
Doubling every part of the body and then splitting into two separate persons strikes me as unrealistic. Humans (or any creature really) need a long time to build up so much tissue, after all this isn't just filling fat cells until you have added 50, 60 kilos. So this would basically amount to a several year pregnancy in which you add another hundred percent of your body weight!
Instead I would consider something akin to the power of a planaria. These flatworms can be cut into up to 50 pieces and every single piece turns into a fully functional worm again. They do this by turning cells back into stem cells and then basically rearranging the complete layout of the little part until a small but viable worm is recreated.
For humanoids this sounds farfetched, but less so if your humanoids have organs that are decentralised and redundant. In that case they might just drop an arm and wait until it turns into a baby …
Let's say if a body part is dropped or cut from the body the skin secretes a kind of cocoon in which the transformation into a baby occurs. That would be similar to the metamorphosis of an insect, which also often involves a switch to a completely new body layout.
Mitosis is a process specific to single-celled organisms. However, there are some multicellular animals, such as planaria and starfish, that are capable of breaking into fragments and regenerating into multiple individuals. Some starfish will fragment proactively as their main means of reproduction.
The main reason why this ability is absent in 'higher' animals is due to the complexity of the central nervous system. Vertebrates have a highly regulated growth pattern with very specific stages from zygote to adult that does not work well unless it develops from start to finish. While some vertebrates have limited regenerative abilities, we cannot grow a whole central nervous system unless we start from scratch.
If a vertebrate were to 'split' in order to reproduce, it would need to grow a new body as a 'bud', starting from a lump of cells and passing through the standard growth stages before breaking off of the parent body. Of course, this would be a lot more inconvenient than just growing a clone inside the body... which is just parthenogenesis.
I asked a somewhat related question in May 2015: What needs to be different in order for a parthenogenetically reproducing species to evolve sentience?
The answers might be useful to you, although they focus on the conditions in which asexual reproduction might dominate rather than on what the mechanics would be. As BlindKungFuMaster has said above there is no obvious reason why the humanoid shape, or sentience, should be a barrier to it occurring. It is rare but not unknown in large animals. It sometimes occurs in komodo dragons and turkeys.
Note that parthenogenesis can occur with or without mitosis, though I confess I don't really understand what "Parthenogenesis can occur without meiosis through mitotic oogenesis" means.