Word for repairing something in a way that changes its function
Solution 1:
You've adapted your washing machine.
Adapt: to change, or to change something, to suit different conditions or uses. [Cambridge English dictionary]
Adapt: Make (something) suitable for a new use or purpose; modify. [Oxford Dictionaries]
Solution 2:
That's called repurposing.
Repurpose (verb): Adapt for use in a different purpose.
Example: They've taken a product that was originally designed for the CD-ROM and repurposed it for the Microsoft Network. [Lexico]
Example: You repurposed the washing machine for cloth-colourer.
If you fix a broken thing and make something else out of it, I suggest Upcycle.
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Transmute would also work well. It means to change something in form, nature, or substance
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Or use customise if you change it according to your needs.
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Revamp, remodel, transfigure and retool could also be used.
I had a bicycle and I changed it to a car.
For this example, I'd use transmogrify.
Solution 3:
How about modify or retrofit? From M-W:
modify: to make basic or fundamental changes in often to give a new orientation to or to serve a new end
retrofit: to adapt to a new purpose or need
Your example:
The washing machine was broken and I modified it in such a way that the function of washing machine is no longer washing clothes but, say, now it colours the clothes.
The washing machine was broken and I retrofitted it in such a way that the function of washing machine is no longer washing clothes but, say, now it colours the clothes.
Solution 4:
The word you are looking for is hack; in its original sense, to fix something into something it wasn't before (or more eloquently, "An appropriate application of ingenuity" )
I didn't need a raclette grill, so i hacked it into a reflow oven.
Solution 5:
To hack something.
(usually used in a software/IT context)
Someone hacked the Make program into an init system.