這句是否省略了 be ?

其實see可以有幾種的結構

以下是Cambridge Dictionary Online舉出的結構並應用

[+ (that)] The teacher could see (that) the children had been fighting.[+ infinitive without to] Jacqui saw the car drive up outside the police station.[+ -ing verb] From the window we could see the children playing in the yard.[+ past participle] His parents saw him awarded the winner's medal.

其他感觀動詞，也有verb+object+ past participle這種結構

而學者Michael Swan就指出，這種結構裏，過去分詞含有被動的意義，如：

I heard my name repeated several times.
Have you ever seen a television thrown through a window?



雖然學者沒有指出這種結構，是否是verb+object+be past particiole將be省略的結果，但相信你的推斷也並沒有錯，因為要表示＂動作和事件在進行＂的概念時，可以用進行式 （being+過去分詞），如：

As I watched the tree being cut down...

I woke up to hear the bedroom door being opened slowly.

但無論如何，我們只需記住verb + object +past participle這結構，是觀感動詞的結構之下即可！

希望幫到你！

saw + 受詞 + 不定式 / 現在分詞，這是正確的觀念

They saw the home team beaten. ，我想知這句是否 They saw the home team be beaten. 的簡寫，這樣認知是可以的。

完整觀念，看這裡(2)。

你第二例句的假設差不多對，過去分詞少了的原因是被動詞(home team是被打敗)，留意第一組的例句動詞是him的主動。

正確的寫法應該是
They saw the home team being beaten.

有些動詞後面，是要使用 infinitive 或 gerund.

而 “see” 後面，可以使用 bare infinitive 、也可以使用 gerund.

問題中的例句：
I saw him leave the building. （leave 是 bare infinitive）
I saw him leaving the building.（leaving 是 gerund）

有些字也會出現同樣的情況，例： hear。

They saw the home team beaten.
是 They saw (that) the home team was beaten. 的另一個寫法。用 phrase 而不使用 clause.