Is there a formula that'll help manage my to-do list?

I keep an agenda at work to manage my ongoing tasks with upcoming deadlines. The agenda is on the left portion of the sheet, and the done pile is adjacent to it on the same sheet.

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When I complete a task, I cut and paste it to the done pile.

But then I'd need to shift up the cells that are below it.

I just feel like there must be a formula that'd automate this.

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For example:

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Column A-D = ongoing tasks

Column F-I = done pile

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Cell A2-D2: Watermelon

Cell A3-D3: Monster

Cell A4-D4: Thugs

...

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"Monster" task is completed.

Cut cell A3-D3 and paste it into the done pile.

Select cells A4-D4 and all cells below and shift up to fill the blank.

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Is there a formula that can...

1. Move a line of cells to a different area of the sheet?

2. Shift up all cells from below to fill the newly blank cells?