It would be nice to have the ability to disable attachments globally in a JIRA Cloud instance - this is currently not possible because it is a Restricted Function in Atlassian Cloud.

Workarounds

• Ensure that users don't have the Create Attachments permission (located inside the permission scheme) for all projects. 
• You can set the max size for attachments to 1 byte in https://<your site name>.atlassian.net/secure/admin/ViewAttachmentSettings.jspa which effectively blocks the uploading of most attachments, but this may cause confusion due to this bug: JRACLOUD-70142 Misleading error related to attachment size