Verb-result compound: 逼 ('press, force') + 死 ('die'). The literal 'driven to suicide' sense is heavy and shows up in news stories about debt, harassment, or workplace abuse. The hyperbolic 'driving me crazy' use is far more common in everyday speech, often with 把 + person + 逼死(了) as the structure.
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When literal, very serious — usually paired with 高利贷 (loan sharks), 上司 (a boss), or domestic abuse. Pop reference: 'X逼死强迫症' ('X drives obsessive-compulsives crazy') is a common online complaint about misaligned UI or poor design.
