Hello,
When my website is under attack, I enable the attack mode through Cloudflare, and the SMTP system (email) on my website stops working. This is very strange, and I have no idea how to solve this situation.
May I ask in which way?
Some forms stop working like WordPress contact forms, etc. or?
Sounds to me like your e-mail (SMTP) related DNS records (hostname) is proxied and set to 
? 
If so, then your e-mail service isn’t working well as expected while you’re using Cloudflare services for your domain name.
May I suggest checking below article if your e-mail records (usually the A mail and the MX record) are configured properly while you are using Cloudflare for your domain name:
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Hello any help ?
You can help us help you by answering the questions put forth by @fritex. You have not provided enough information for anyone to offer any further assistance.
I don’t see any obvious issues in a quck review of your DNS. The ftp hostname being could be problematic if you expect to use it with non-HTTP protocols, but that is unrelated to this topic. Your CAA records are also outside of this topic, but are also curious.
How does your site send email?
Are you using HTTPS API calls to Twilio Sendgrid?