Some schools for a variety of reasons require a teacher to hand over their blog to another teacher. It often is because the blog was named "room10crazyschool.blogspot.com" etc.
And now the teacher has to swap classrooms and isn't allowed to keep the URL because they are going to be in "room19crazyschool.blogspot.com".
Or they had the "Maths" blog and now they are the "Calculus" teacher.
On occasion a teacher leaving the school very generously allows their new replacement to benefit from all their hard work and donates not only the blog, but also all the good will and connections associated with the blog, to the next teacher.
So what to do?
First, BOTH teachers need to respect the student's right of ownership of the content and DON'T delete it!
This work, if tagged correctly, has become part of the student's digital footprint (ePortfolio) and they deserve to have it preserved.
The leaving teacher
Should post a sign off post, with a positive farewell AND leave a link if possible to the new blog they are creating. I would take a screen shot of the current blog, to preserve it for nostalgia, and include that image IN the final post.
The new teacher
It would be a nice touch to start with a post of thanks to the leaving teacher and explain that new things are happening because the blog is under new management.
Then give the blog an update and makeover.
Alter the contact information, the about me, the email addresses in the settings, etc
Makeover the theme or skin, change the name of the blog etc
DON'T delete student posts. Even if they do not reflect your philosophy or standards, they belong to the students. And if you have started out well introducing yourself, no-one will hold you to account for the previous work!