The best replacement for mandamus is injunction.

The best alternatives to mandamus are rated as following:
★★★★★  injunction
★★★  prohibition
★★  mittimus
★★  mandamus
★  interlocutory appeal

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Speaking about mandamus, one probably shouldn't forget about certiorari.

Other search terms related to mandamus and their ratings are:
★★★★★ certiorari
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mandamus
injunction
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