As I understand your question, this is a person who can not do the work themselves, and really needs it to be done as soon as possible. My week is "booked" so that the only time to do it is Sunday afternoon. Is it a work of mercy?
I would say, YES--it is a work of mercy and therefore could be done on the Sabbath.
But, it would not be my first choice...and I would (and have in the past) rearrange my week so that I could do it on Monday, regardless of what I had planned previously for that day.
But, perhaps that's just me. My family has gotten use to idea that this deacon sometimes puts such mercy needs of God's people ahead of some other duties and responcibilities. It is a sacrifice we are sometimes called to make for the advancement of His kingdom. ANd since it involves yardwork, I would most likely have my son working along-side me. It is good to teach our children that the needs of God's people come before our own.

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Sterling Harmon
Coventry, CT
PCA
Deacon
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"Whatever is laudable in our works proceeds from the grace of God."
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John Calvin, Institutes III:xv.3.
"Our Lord God must be a good man, to be fond of worthless fellows. I cannot like them, and yet I, myself, am one."
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Martin Luther, Table Talk