Opposite

What is the opposite of 注意しすぎてもしすぎることはない?

Is it 注意しすぎのことがある？

例えば：体を注意しすぎなら、ストレスが一杯になる。

Thanks for your help!

That sentence (though a bit strange) intends to say "You can't be too careful." "You cannot be excessively careful." (So, do be careful as much as you can.) It should be something like:
いくら注意しても、注意しすぎることはない。(No matter how careful you are, you cannot be over-careful.)

What do you want to say, when you say "the opposite"? Just "You don't have to be careful at all"?

注意しすぎてもしすぎることはない

This sentence reminds me of a Japanese saying
石橋を叩いて渡る

which means "bang the stone bridge before you cross it" or "Look before you leap".

The opposite of 石橋を叩いて渡る is a parody of the saying,
石橋を叩いて壊す which means "bang the bridge to break it."

The literal opposite of 注意しすぎてもしすぎることはない
should be

注意しすぎということもある or
注意しすぎることもある

If what you are trying to say was like "Care killed a cat", it would be " 病は　気から"?