This may help: https://www.hometalk.com/41039225/easiest-way-to-clean-your-mattress
Rent a carpet shampooer and use the upholstery attachments. Pretreat with stain remover like Resolve.
You'll likely need a small carpet spot cleaner but you could do it using some peroxide which will get rid of blood stains in clothing but it could bleach the mattress. Start with a small amount to dampen the stain and wait 5-10 minutes and then apply a little more. Dab at it with a clean cloth or paper towel between adding more peroxide.