The Apple Time Machine feature does indeed keep copies of your files after deleting files. That is its purpose, remembering what your drive looked like in the past. Thus the name Time Machine.
Just use a large drive for your Time Machine. Copies of your changed files are kept on an hourly, weekly, and monthly basis endlessly until the drive is full. If its drive fills up, Time Machine must delete old files to make room for newly changed files.
You may not want Time Machine to copy everything. Perhaps some files contain sensitive matters, with privacy concerns. Or some files such as virtual machines (Parallels, Fusion, VirtualBox, etc.) are so huge that keeping versioned copies would quickly fill the Time Machine drive, defeating its purpose of keeping long-term copies of all files. To omit such files from your Time Machine backups, use the
Time Machine System Preferences
Privacy panel to make a list of such files or their folder.
In theory you can recreate your bootable system on a new drive from the Time Machine. In practice, people report mixed results. Personally I use Time Machine only for retrieving individual files, and never depend on it to restore my entire hard drive.
For restoring an entire drive, I clone the drive. On occasion, such as before a travel trip, I make an clone copy of the entire drive on to another drive (reformatted using Apple’s Disk Utility app). To make such an exact clone, I have used either of these two Mac apps. Both work very well to create a bootable backup of a startup drive.
(free-of-cost for basic manual cloning features, USD $28 for advanced features such as automated scheduling and scripting)
- Carbon Copy Cloner
(USD $40 after free trial)
You clone into a second drive. Fortunately they are inexpensive now, a few tens of USD dollars for a terabyte. You may need to obtain an external case or a drive dock to hold the drive.