Is using Tommee Tippee microwave steam sterilizer safe? does it cause cancer bcz plastic?

Short answer: yes, it is safe.

Tommee Tippee microwave steam sterilizer is really made from "BPA free" plastic, and the risk of migrating chemicals (process when chemicals from plastic or any other materials "migrate" from one form to another, such is from steam sterilizer to baby bootle) are almost non-existing.
All steam sterilizers are made from plastics that has been tested for chemical migration during planed operation(i.e. microwaving it for short and long period of time), and Tommee Tippee is a reputable manufacturer so they must have very good quality control.
You can read more about dangers from Migrating chemicals on http://www.health.harvard.edu/staying-healthy/microwaving-food-in-plastic-dangerous-or-not

On the side note, from one parent to another: take consideration that your baby must develop its own immunity, and to do that, it must be exposed to a healthy level of bacteria, even in its early days. So, if your baby is healthy, reconsider using steam sterilizer, and help him/her to develop that needed immunity.
This advice does not apply if your baby is sick, having a common cold(or any other virus) - in that case, this sterilizer will actually very much help to minimize other exposures and help the body to fight against the current virus/bacteria that he/she is suffering from.