按照以下思路理解，就行了。

grieved 是形容词（悲伤的；难过的；伤心的）；

be grieved 是“系表结构”；

being grieved 是动名词短语作介词without 的宾语。

I can never be in company with this Mr.Darcy without being grieved to the soul by a thousand tender recollections

我永远不能和这位达西先生在一起，除非有一千种温柔的回忆使我对灵魂感到悲伤。

解析如下：

without being grieved to the soul by a thousand tender recollections

以上属于介词+动名词被动结构构成介词短语。句子属于双重否定表示肯定

grieve可以是不及物动词，可以为及物动词

(1)grieve vi.（尤指因某人的亡故而）悲痛，悲伤，伤心

He's grieving over his dead wife and son.

他因丧妻失子而悲痛不已。

I didn't have any time to grieve. 

我没有时间伤心。

Margery's grieving family battled to come to terms with their loss. 

玛格丽万分悲痛的家人努力从丧亲之痛中恢复过来。

grieve vt.使难过；使悲伤(sb be grieved by )

He was deeply grieved by the sufferings of the common people.

百姓的困苦使他痛心不已。

I was grieved to hear of the suicide of James.

听到詹姆斯自杀的消息，我非常伤心。

It grieved me to see the poor man in such distress. 

看见这个可怜的人如此困窘，我很难过。