I can think of 2 relatively easy methods to send an anonymous email. Be careful to not abuse these methods, otherwise, the email service providers herein might decide to restrict or block global access to such services permanently. Use prudence and good judgement when sending anonymous emails. In most jurisdictions, it is a serious crime to send emails that threaten or harass or contain other illegal content. It is easy to inadvertently leave tell-tale clues in the Subject line or message body of an anonymous email that could give away your identity. A combination of unique elements such as the type of language, grammar, vocabulary, font, style, and other elements you use in the email have the potential to trace back to you.
Configure Tor browser ▸ Privacy and Security Settings ▸ Tor Network Settings to the highest level. In Tor browser ▸ Network Settings ▸ Enter custom bridges, consider using the most obfuscated (most secure) type of custom bridge address, obfs4. (The only other type of bridge address that might be more secure is a private obfuscated bridge address that a trusted friend gives to you, but not to the public, after your friend sets up a private Tor bridge relay.)
Use Tor browser to connect to StartMail. Open a free 7-day trial account. Your name, phone number, email address, or other personally identifying information are not required to open the account. Configure your preferred user account settings. Send your anonymous email. The only sender IP address that will appear in the full email header will be the IP address of the StartMail email server. The email header will not include your IP address, your name, your country location, or any other personally identifying information about you. The email service provider will be unable to log or record your IP address if you are using the Tor browser with the highest Privacy and Security Settings and an obfuscated bridge address.
With Tor browser, connect to Yandex mail. Open an email account. Your name, phone number, email address, or other personally identifying information are not required to open the account. Configure your preferred user account settings. Send your anonymous email. The only sender IP address that will appear in the full email header will be the IP address of the Yandex email server. The email header will not include your IP address, your name, your country location, or any other personally identifying information about you. The email service provider will be unable to log or record your IP address if you are using the Tor browser with the highest Privacy and Security Settings and an obfuscated bridge address.
In contrast to the StartMail free 7-day trial account, a personal paid subscription to StartMail email service does not provide 100% anonymity, although, to the best of my knowledge, it does provide the highest level of anonymity and privacy from a commercial email service provider that includes a built-in option to send and receive PGP encrypted emails. Additionally, the StartMail organization is in the Netherlands, beyond the legal jurisdiction of any foreign governments. See the StartMail Policies, Technology, and Privacy statements for a better understanding of the practices and methods that StartMail uses to protect a user's personal information, privacy, and anonymity, including guaranteed no tracking or advertising and regular automatic deletion of some of the users' personal information within hours after the session ends.
(Note: the following info about the sister StartPage and Ixquick Internet search engines does not relate directly to sending an anonymous email, but since StartMail, StartPage and Ixquick are all parts of the same parent organization in the Netherlands, it might be worth noting this info because it relates directly to Internet anonymity and privacy. The StartPage and Ixquick Internet search engines provide superior anonymity and privacy, especially if you connect to the sites with the Tor browser. The servers use advanced SSL encryption for all Internet connections to the servers. The servers provide all users the option to establish a free, instantaneous, and certified anonymous proxy Internet connection with the server of any web site in the Internet search results. The servers do not collect or share any personal information. The servers do not log legitimate users' IP addresses, and do not record or save users' Internet search activities or search results. The search engines use the so-called POST method (instead of the GET method) to keep your search terms out of the logs of webmasters of sites that you reach from the search results. Settings gives all users the option to save a user's preferred page settings without using a cookie. The referenced servers herein are in the Netherlands beyond the legal jurisdiction of any foreign governments. For a better understanding of practices and polices regarding anonymity and privacy, see StartPage Protects Your Privacy!, Privacy Q&A, and Our privacy policy.