Donald Trump swept to victory in Tuesday’s Republican caucuses in Nevada, following his primary triumphs in New Hampshire and South Carolina.

【翻译】唐纳德·特朗普，继新罕布什尔州和南卡罗来纳州的初选胜利后，又在周二内华达州举行的共和党党团会议上，大获全胜。

【分析】following his primary triumphs in New Hampshire and South Carolina 为现在分词短语，作伴随或者方式状语，逻辑主语是Donald Trump。

sweep to victory 是个习语，意为“大获全胜”。

从动作发生先后关系看，his primary triumphs 在先，swept to victory 在后。因为swept to victory 是following his primary triumphs。