Nevermind...I'm an idiot. Just forgot to catch the return of the Open(). Adding nul= in front solved the issue.

 Code:
Break On

$DrawingFile = @ScriptDir+"\Drawing1.vsdx"
$date = Join(Split(@Date,"/"),"")
$ext = SubStr($DrawingFile, InStrRev($DrawingFile,"."))
$newDrawingFile = Split($DrawingFile, $ext)[0] + "_" + $date + $ext


$oVisio = CreateObject("VISIO.InvisibleApp")

$nul = $oVisio.Documents.Open($DrawingFile)

$textBox1 = $oVisio.ActiveWindow.Page.Shapes.ItemFromID(1).Characters
$textBox1.Text = "987654321"

$nul = $oVisio.ActiveDocument.SaveAs($newDrawingFile)

$oVisio.Quit
$oVisio = 0