This quote seems to come from a document explaining Buddhist teachings, put together by an organization called The City of Ten Thousand Buddhas, a monastery in Talmage, California.
In that text we find the following, which refers to the Buddha:
He discovered three great truths. He explained these truths in a simple way so that everyone could understand them.
1. Nothing is lost in the universe
The first truth is that nothing is lost in the universe. Matter turns into energy, energy turns into matter. A dead leaf turns into soil. A seed sprouts and becomes a new plant. Old solar systems disintegrate and turn into cosmic rays. We are born of our parents, our children are born of us.
We are the same as plants, as trees, as other people, as the rain that falls. We consist of that which is around us, we are the same as everything. If we destroy something around us, we destroy ourselves. If we cheat another, we cheat ourselves. Understanding this truth, the Buddha and his disciples never killed any animal.
I could quibble with the statement that the Buddha formulated a truth that “nothing is lost in the universe” — I suspect that insight is borrowed from modern physics, and that the BUddha said no such thing — but my point here isn’t to critique the article, just to show it as the probable origin of this quote.
“We are the same as plants, as trees, as other people, as the rain that falls. We consist of that which is around us, we are the same as everything” is a quote I’ve dealt with elsewhere.
“If we destroy something around us, we destroy ourselves. If we cheat another, we cheat ourselves” certainly strikes me as a wise perspective to hold.
However, this document clearly isn’t a Buddhist scripture, and isn’t claiming to represent what the Buddha said. It seems that someone has taken this quote and either accidentally or deliberately presented it as something the Buddha said.
It’s of course impossible to create without destroying: in order to grow food, for example, we have to clear the land, break the ground, and (no matter how careful we are) kill worms and insects. Rules for monks and nuns were stricter, since they didn’t have to work.
Lily de Silva has an article on Access to Insight on Buddhist attitudes to nature that gives a hint as to the care that monks were expected to take.
The Buddhist monk has to abide by an even stricter code of ethics than the layman. He has to abstain from practices which would involve even unintentional injury to living creatures. For instance, the Buddha promulgated the rule against going on a journey during the rainy season because of possible injury to worms and insects that come to the surface in wet weather. The same concern for non-violence prevents a monk from digging the ground.
De Silva also talks about attitudes to plants:
Buddhism expresses a gentle non-violent attitude towards the vegetable kingdom as well. It is said that one should not even break the branch of a tree that has given one shelter. Plants are so helpful to us in providing us with all necessities of life that we are expected not to adopt a callous attitude towards them. The more strict monastic rules prevent the monks from injuring plant life.
Householder Buddhists were of course in a different position. Many of them would have been farmers and would had to cut down trees, harvest crops, etc. And it would have been unavoidable that they killed small creatures while plowing the land and so on. But even then they weren’t supposed to kill or cause to kill animals. The general idea would have been to minimize the amount of destruction to living things in order to prevent suffering:
All tremble at violence,
All fear death;
Comparing oneself with others
One should neither kill nor cause others to kill.
(Dhammapada Verse 129)