Q:

How to clear the file contents after reading

The operation of reading data and the subsequent cleaning of the file must be in one session.  and other processes should not have access to the file. 
$FileTwo = [System.io. File]::Open('C:\FiLeTwo.txt', "Open", "Read", "None") 
$FileTwo2 = New-Object System. IO.StreamReader($FileTwo)
$text = $text + $FileTwo2.ReadToEnd()

$text = $text -replace '\ ' -replace 'g' -replace '\(' -replace '\)' -replace $re, "" #-replace '\n'
# Set-Content 'C:\FiLeTwo.txt' "" -Force 
# IN that moment I need to clear the file.  
# But I need cleare the file and,  after, close the File ($FileTwo. Close())

$FileTwo. Close()

A:

You don't even need to use so many streams:
$path = 'C:\FiLeTwo.txt'
$text = Get-Content $path -Raw
Clear-Content $path
$text = $text -Replace ...

If you want to use a FileStream, you can also use SetLength to erase the contents:
# open with "ReadWrite"
$fileTwo = [System. IO.File]::Open("C:\FiLeTwo.txt", "Open", "ReadWrite", "None") 
try {
    # ... read, replace etc ...
    # clear the contents:
    $fileTwo. SetLength(0);
}
finally {
    # make sure to put this in a finally block! 
    $fileTwo. Dispose()
}

(Make sure to dispose all your streams properly in a finally block!)