It' an old saying that"It is not that you say but what you s

首先,你这句话不准确,应该是：It' an old saying that"It is not what you say but how you say it that matters." 意思是：俗话说,重要的是怎么说,而非说什么.
其次,这是一句多重复合句.
1.主体是同位语从句,主句It' an old saying,从句that"It is not what you say but how you say it that matters."
2.从句其实是强调句,强调的部分是not what you say but how you say it
3.强调的部分又是由并列的两句主语从句not what you say和 but how you say it 组成的,它们共同的谓语动词是matters.

应该是It is not what you say but how you say it that matters.首先这个句子是个同位语从句，先行词为the saying，也就是这句解释说明the saying。
分析It is not what you say but how you say it that matters，是 not what you say but how you ...