They had the capability to detatch individual nacelles:
Ed Whitefire's original blueprints for the Enterprise-D, which were used as a basis for Rick Sternbachs official version, contain "Warp Nacelle Emergency Disconnects". These are, however, at the top of each pylon and not where the image in the question shows.(Click for full image)
From the official Rick Sternbach drawings, we see the Warp Nacelle Emergency Disconnects have been removed, however he's kept the same design for the explosive bolts, although hasn't labelled them. (Again, click to embiggen)
As further outlined in the comments from the Technical Manual, the nacelles could be ejected at a speed of 30m/sec. Note in the official drawing above the ten explosive latches which were marked on the original as "explosive bolts".
But only saucer separation is seen on screen:
After a warp core breach, where LaForge confirms there's nothing he can do, the separation sequence for the warp core begins:
LAFORGE: Coolant leak! We have a coolant leak, everybody. Let's go. Let's get out of here. ...Everybody out! Let's move! ...Let's move! Let' go! Bridge, we have a new problem. We're five minutes from a warp core breach. There's nothing I can do.
RIKER: Deanna, evacuate everyone to the saucer section. Mister Data, prepare to separate the ship
After everyone has been evacuated into the saucer section, Data completes the ejection and confirms so:
DATA: One minute to warp core breach.
RIKER: Begin separation sequence. Full impulse power once we're clear. Warp core is going critical.
DATA: Separation complete.
TROI: Engaging impulse engines.
DATA (OC): Core breach in progress.
COMPUTER VOICE: Primary stabilisers off-line. Engaging secondary systems.
TROI: Helm controls are off-line!
DATA: Oh, shit...
(on the viewscreen Data has realised the saucer section is hurtling towards the planet)