TAR gives error – tar: You may not specify more than one `-Acdtrux’ or `–test-label’ option

As others have identified, the problem with your command is that it includes directories, and tar archives them recursively. If a directory has been modified recently, all the files in it and its subdirectories get included, whether they have been modified or not.

If you don't care to back up directory metadata, then just tell find not to print directory names. It isn't enough to omit the root: the same thing can happen with subdirectories too.

find "$SOURCEDIR" -mtime -1 ! -type d -print | xargs -r tar -rcf "$ARCHIVE"

Using xargs fails with file names containing spaces and some other special characters. This is easy to fix: use -exec instead of xargs.

find "$SOURCEDIR" -mtime -1 ! -type d -exec tar -rcf "$ARCHIVE" {} +

If you want to back up directory metadata, let find print everything and instead tell tar not to recurse into subdirectories. Since find is doing the recursion, tar doesn't need to.

find "$SOURCEDIR" -mtime -1 -exec tar -rcf "$ARCHIVE" --no-recursion {} +

With this approach, you can avoid the use of tar -rc and instead solve the problem of repeated tar invocations by first creating an archive with only the root directory, and then appending to it in batches. (Why the root directory? Because GNU tar is afraid of creating an empty archive.)

tar -cf "$ARCHIVE" --no-recursion "$SOURCEDIR"
find "$SOURCEDIR" -mindepth 1 -mtime -1 -exec tar -rf "$ARCHIVE" --no-recursion {} +

You are not specifying an archive in your statements. It should look something like:

tar -cvf tar2/tar1.tar tar1/

This places the tarball tar1.tar inside the directory tar2/.

Before:

tree tar*
tar1
├── a.txt
└── b.txt
tar2
├── a.txt
└── b.txt

0 directories, 4 files

After:

tar -cvf tar2/tar1.tar tar1/
tar1/
tar1/a.txt
tar1/b.txt

tree tar*
tar1
├── a.txt
└── b.txt
tar2
├── a.txt
├── b.txt
└── tar1.tar

0 directories, 5 files

Environment:

Distributor ID: Debian
Description:    Debian GNU/Linux 8.6 (jessie)
Release:    8.6
Codename:   jessie