There are two ways to do this:

First, when viewing an error in the Backtrace debugger, you can click on the download icon on the upper right and select the "snapshot" format to download the minidump:

Second, you can do this via the command-line with the morgue  tool:  https://github.com/backtrace-labs/backtrace-morgue

The command is:  morgue get projectname objectid -o /path/to/output.dmp 

You can get the objectid by looking at the error within the Backtrace UI, it appears at the end of the URL when viewing an error in the debugger (debugger/objectid )

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