Usually you would use option 2.
Example:
I have done my homework and put my textbooks back in my backpack.
(Note that, as 'Jason Bassford Supports Monica' says, it is pretty rare to use "put" as a verb all by itself without some kind of preposition or additional wording, like: "put away", "put back", "put the lid on", etc.)
The helping verb "have" can be stated just once with the first verb ("done"), and when a second participle comes up in the sentence ("put"), you don't need to repeat the "have" because your audience knows to apply the same helping verb to that participle too.
But, your first option (repeating the helping verb), is not incorrect, and you might want to state your sentence that way for emphasis.
Example:
"I have made this announcement four times and have gone out of my
way each time to make sure that everyone was informed."
You could also say:
"I have made this announcement four times and gone out of my
way each time to make sure that everyone was informed."
The second sentence is a simple statement of fact, but the first one, with its redundant helping verb, sounds a little more emphatic, and the impatient emotional content is more noticeable.
If you repeat both the subject and the helping verb, turning the statement into a compound sentence:
"I have made this announcement four times, and I have gone out of my
way each time to make sure that everyone was informed."
it sounds even more emphatic and (in this case) exasperated.