Here's the man page for mdutil:
mdutil(1) BSD General Commands Manual
NAME mdutil -- manage the metadata stores used by Spotlight
SYNOPSIS mdutil [-pEsav] [-i on | off] mountPoint ...
DESCRIPTION The mdutil command is useful for managing the metadata stores for mounted volumes.
mdutil(1) BSD General Commands Manual
NAME
mdutil -- manage the metadata stores used by Spotlight
SYNOPSIS
mdutil [-pEsav] [-i on | off] mountPoint ...
DESCRIPTION
The mdutil command is useful for managing the metadata stores for mounted volumes.
The following options are available:
-p Spotlight caches indexes of some network devices locally. This option requests that a local
caches be flushed to the appropriate network device.
-E This flag will cause each local store for the volumes indicated to be erased. The stores will
be rebuilt if appropriate.
-i on | off
Sets the indexing status for the provided volumes to on or off. Note that indexing may be
delayed due to low disk space or other conditions.
-s Display the indexing status of the listed volumes.
-a Apply command to all volumes.
-v Print verbose information when available.
I would use:
mdutil -E -i off [the mountpoint for your backup drive]
mdutil -E -i off [the mountpoint for your backup drive]