Is science destroying the way we live?

That's not quite an accurate depiction of "cloning". Cloning simply means a genetically identical copy. Much of cloning techniques currently used are at the micro-biology level to clone genes using bacterial replication mechanisms. Therefore it is a very useful tool in genetic research.

The way I understand it, it seems like a lot of controversy comes from a question of whether scientists are ethical enough to handle the power that comes with being able to use stem cells to grow new tissues. There is much good that can be derived from using stem cells, and to restrict research completely in that direction would lose much in potential cures and treatments. The scientists engaged in this research are not there to try to grow new species of humans, they are trying to find a viable alternative (for example) for people in desperate need of organ transplants.

Stem cell research and cloning do go hand in hand, because any tissue you grow from a stem cell are derived from that stem cell, and by definition of how mitosis (cell division) works, they are, in theory, all clones of the original stem cell.

I don't think science is destroying the way we live. Is there not something magical as well in being able to figure out how stuff works? And even if we are all composed of the same particles, is it not miraculous how very different we all are, despite that?

Well, the issue is not with cloning microbes or something, I am talking about some people wanting to clone humans. The promises of that are extreme, but if that's not playing God I don't know what is. In the past, horrifically unethical methods yielded tremendous advancement. It's not publically fashionable to discuss, but the Allies bought Nazi and Japanese war criminals' scientific research with cash and immunity from prosecution, (the research done on concentration camp victims and victims in the Japanese conquered territories and usually caused death.) In less extreme cases, you have the Milgram Experiment and the Stanford Prison Experiment, both psychological studies done before the modern rules of ethics were put in place, both horribly unethical, and both yielding a wealth of information about human nature. Ethics is a huge deal because we can do a lot by crossing the line, but allowing that sort of thing has the same implications on society as democracies going Gestapo on problematic minorities.