When creating a new email campaign, one of your first steps is to determine who should receive the email. This is typically done by creating a report in Salesforce that has filters built into it to include only the correct people in the campaign. Since Soapbox Mailer is meant to be a flexible tool for sending emails of all kinds, it does not include a pre-built system for managing the exclusion of Contacts that have reported spam complaints in the past. This allows your organization to manage complaints as you see fit, through a variety of data architecture choices.
One easy way to exclude people from campaigns is to filter by a date/time field on the Contact. When a spam complaint comes into Soapbox Mailer, you could write a trigger or a Process Builder flow that will go to the Campaign Member's existing Contact record and update the spam complaint field with the date/time of the spam complaint. Then, you can create your report to only include Contacts that do not have a value in that particular field.