Tumblr respects your privacy and allows you to Block Someone who are associate in harassment or spamming. If someone make such activity with you, You can easily block them.
Above is just a screenshot which i have taken to show you how to block someone on Tumblr.
How to Block People on Tumblr
Look, I believe, Tumblr has more secure and protected privacy feature comparing to other social media network and blogging networks. In the case, If someone harass you or making spam on your ask, You have option to block them by getting notification and viewing your blog when they are logged in.
You just need to point your web browser to blocking page and there you will be asked a URL of a User to whom you want to block.
More clues and details about Block Someone can be found here.