The disc falls straight down into the glass when you quickly pull the index card away because of inertia.
Inertia is the property of matter that causes it to resist changes in its state of motion. When you quickly pull the index card away, the disc was at rest and due to inertia, it tends to remain in its state of rest. Since the index card is removed quickly, the disc is no longer supported and falls straight down into the glass under the influence of gravity.