The reasons why you want to delete a post on Tumblr can be many: it is not as interesting as you thought, you posted it by mistake, you have had legal problems (for example related to copyright) … Luckily it is quite easy to do so.
Steps
Step 1. Open the dashboard
After logging in, you will be redirected directly to the dashboard. If you are on another Tumblr page, click the Dashboard button at the top right.
Step 2. Click the Account button
It is located in the upper right, to the left of the blue Create a post button. Clicking on the button, a drop-down menu should open.
Step 3. Click on the Post button
It is located under the "Tumblrs" tab in the drop-down menu you opened. You will be redirected to a list of all your posts.
Step 4. Find the post you want to delete
The publications will be sorted chronologically, so you simply have to scroll until you find the unwanted one.
Step 5. Click the gear button
It is located at the bottom right for each post. A small menu will open.
Step 6. Click the Delete button
Step 7. Click the OK button
This will delete the post.
Advice
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You can open the "Posts" page in one step using the following URL, where "blog-name" should be replaced with your blog name. Remember that you must log in before proceeding.
https://www.tumblr.com/blog/blog-name