To add to @Locksleyu's answer, 出す in "the continuative form of a verb (動詞の連用形) + 出す" can mean either:
㋐ そうすることによって外や表面に現れるようにする意を表す。「しぼり―・す」「見つけ―・す」
to make something reveal/appear outside or on the surface by doing the action, eg 「しぼり出す」(squeeze out) 「見つけ出す」(find out)
or
㋑ その動作を始める意を表す。「降り―・す」「笑い―・す」
to start the action, eg 「降り出す」(start to fall/rain) 「笑い出す」(begin to laugh)
(Source: 「出す」 #4(動詞の連用形に付いて) in デジタル大辞泉)
The 出す in [救]{すく}い出す is used in the sense of ㋐, "to save/help (someone) out (of somewhere / trouble / difficult situation)", rather than "start to help."
Here are some more examples:
㋐:
[取]{と}り出す -- take out
[引]{ひ}き出す -- pull out
[呼]{よ}び出す -- tell (someone) to come; summon
[助]{たす}け出す -- help (someone out of...)
㋑:
[泣]{な}き出す -- start to cry
[歩]{ある}き出す -- start to walk
[歌]{うた}い出す -- start to sing
(Some ~~出す compound verbs have both meanings, eg 逃げ出す can mean ㋐ get away from... / out of... ㋑ start running away)