处 here is read chǔ (3rd tone, 'to handle / sentence'), not chù (4th tone, 'place'). The construction 处以...刑 ('sentence to ... punishment') is common in legal language: 处以死刑 (death penalty), 处以罚款 (fine).
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Formal/legal. In modern Japanese-influenced fiction (anime, manga 处刑シーン), 处刑 specifically connotes execution; in legal Chinese it means 'sentence' more broadly.