Is it permissible to create a link-shortening website, knowing that visitors may use it for both permissible and impermissible things, and would the website owner's disavowal and monitoring of violating links make its creation permissible?

The owner of a website is directly and primarily responsible for all content published on it. They must prevent the publication of materials that violate Islamic law. If they are unable to prevent forbidden content, then it is impermissible to create the website, and there is a concern that they may be sinful for its publication. Merely warning against forbidden content without removing it is insufficient and does not absolve one of responsibility. However, if a warning is issued and there is regular monitoring and removal of violations, then it is hoped that one's responsibility will be absolved thereby.