What is meant by 'take off' here in this context? ?

Get rid of the first "off." You only need one "off." Get rid of the meaningless "here" while you're at it. You can spare "just like that" and "that you deal with" too.

"This bot will take all the tedious tasks in you daily routine off your shoulders." Of course if you're getting paid by the word, throw in all the unnecessary words you desire.

it is a poorly written sentence: "take off (things) off your shoulders."  It should be either take off things...  or take things off your shoulders, but not take off things off...

Take off (your shoulders) just means "remove a responsibility", remove a burden.

You only need, and should only have, the word "off" once.

Substitute the words take off and replace them with REMOVE.

"The bot here is going to___ all the tedious..."

- remove

- eliminate

- get rid of 

The first "off" shouldn't even be there.

It has too many “off”s.    The phrase the writer was trying to use is “take off your shoulders,” which means “relieve of responsibility.”  Many words separate the phrase in this example, and that’s one reason it doesn’t work here.  A better example:  This bot will take all your tasks off your shoulders.

It's a very badly worded sentence, but basically "take off" in this case means automate.