You can configure a separate file group for this table, except for the PRIMARY file group. This will give you the opportunity to create a backup that omits your large table. The following is an example that fixes this process.
1) .
USE [master]
GO
ALTER DATABASE [EXAMPLEDB] ADD FILEGROUP [EXAMPLEFG1]
GO
2) .
CREATE TABLE [dbo].[example]
(
[e] [int] NOT NULL
)
ON [EXAMPLEFG1]
GO
3) .
4) .
5) PRIMARY, , "EXAMPLEFG1".
BACKUP DATABASE EXAMPLE
FILEGROUP = 'PRIMARY',
TO DISK = '<Your Directory>'
GO
EXAMPLEFG1
FILEGROUP "EXAMPLEFG1" .
Microsoft .
, !