To be swamped with work; to become extremely busy and overwhelmed with tasks.
今月は締め切りが重なって忙殺されている。
This month I'm swamped with overlapping deadlines.
彼は新しいプロジェクトに関わってから忙殺される日々が続いた。
Since getting involved in the new project, he has had days of being completely swamped.
年末は忘年会や報告書で忙殺されがちだ。
At year-end one tends to be swamped with parties and reports.