of saying that

The verb "accuse" is usually used with "of" in the following pattern:
Someone "accused" another person "of" doing something (wrong).

In this sentence, "of" is the preposition that works with "accused", to identify that the subject of the noun clause "saying that poverty could not be completely eradicated." is Mr Leung.

Without the "of", the subject of the noun clause "saying that poverty coiuld not be completely eradicated" is Mr Lee, and that Mr Lee simply accused Mr Leung, but did not specify what the accusation was, and Mr Lee then said poverty could not be copletely eradicated. This is obviously not the intention of the sentence, which states that Mr Lee accused Mr Leung, of saying something inappropriate.

句子的主要結構是
Mr Lee accused someone.
而accuse的內容是「關於」/「關乎」他的言說/說話...
所以這of的作用是表達關於他的甚麼...
因為accuse這動詞所及的東西可以是人格/行為/說話/等等不同對這人物附屬的性質，句子結構上假如如你問的直接someone saying...之後的句式應該亦要改變為直接講述而不是用第三身的"that"作為記述：
Mr. Lee accused (someone) saying, "Proverty cannot be completely eradicated."
而不能單單減去of.

從句子表達的角度，accuse (someone) of "gerund"是格式，例如"gerund"可以是stealing等等已經完成句子了。

這只是針對你問題的回答，未必能涵蓋所有句子文法上的結構。