Among volcanologists, "table mountain" is a term applied to a specific type of landform that is produced by subglacial eruptions:

Volcanoes and Tectonics of Iceland
"Iceland was buried under ice in the last Ice Age and all eruptions were subglacial. Remnants of the ice caps remain and Iceland continues to have numerous subglacial eruptions. Of the world's known subglacial eruptions, 83% are in Iceland. The most recent eruption, at Grimsvotn, is an example. Subglacial eruptions produce a special type of volcano, called a table mountain or a moberg mountain. Great volumes of meltwater, generated by subglacial eruptions, can burst out from beneath glaciers to produce enormous floods called jokulhlaup. The discharge can be as much as 20 times greater than the flow rate of the Amazon River."
http://volcano.und.nodak.edu/vwdocs/volc_images/europe_west_asia/iceland/iceland.html

Other common names for this volcanically produced landform are stapar (plural stapi) and tuya:

SOUTHWEST ICELAND
"Iceland hosts a variety of unique landforms developed by extrusion under the ice caps (Preusser, 1976; Williams et al., 1983). A dominant form is the serrated ridge produced by subglacial eruptions where lava enters long fissures under the ice, Another is the stapi or table mountain, of which those at Eiríksjökull (Figure V-15.1 (B)), Thórisjökull (C), Geitlandsjökull (D), Bláfell (E), and Hrútafell (F) are outstanding examples that cluster about the icecap, Langjökull. A stapi results from "intrusion" of lava into glacial ice cover which, on melting, helps to mold the volcanic materials against the ice-wall void. Stapis have steep slopes and flat tops built from palagonite breccias capped by subaerial basalt."
http://daac.gsfc.nasa.gov/DAAC_DOCS/geomorphology/GEO_3/GEO_PLATE_V-15.HTML

Subglacial volcano shapes
"If the volcano was not hot enough to melt through the overlying ice cap, a subglacial mound would be all that remained of the volcano once the ice had retreated (e.g. Fig.22, Fig.23, stage 2b). However, if the volcano was hot enough to melt through the overlying ice cap, more-normal-looking, subaerial (formed in the air) lava flows might flow out on top of the pillow lavas and cover them up. Once the glaciers had retreated or melted away, the steep-sided and in places flat-topped volcanoes would reappear with a unique shape as a result of their confinement within glacial ice (Fig.23, stage 3b). Dr. Mathews referred to these flat-topped, subglacial volcanoes as 'tuyas' after Tuya Butte in northern British Columbia where he first studied these unique volcanic forms. Similar mountains in Iceland are called 'table mountains' because of their flat tops."
http://www.nrcan.gc.ca/gsc/pacific/vancouver/volcanoes/03_8_typ_e.php

Such mesa's seen on Mars had earlier been suggested to be due to subglacial volcanism from Viking era images:

Title: Volcano-ice interactions on Mars
Authors: Allen, C. C.
Journal: Journal of Geophysical Research, vol. 84, Dec. 30, 1979, p. 8048-8059.
http://adsabs.harvard.edu/cgi-bin/bib_query?1979JGR....84.8048A [abstract]

Title: Table Mountains of Mars
Authors: Hodges, C. A.; Moore, H. J.
Journal: LUNAR AND PLANETARY SCIENCE IX, PP. 523-525.
http://adsabs.harvard.edu/cgi-bin/bib_query?1978LPI.....9..523H [full
text]

To confirm they are table mountains there are certain spectrographic signatures you could look for, such as for example hematite expected in a hydrothermal environment. And also the volcanic rock rhyalite.

Bob Clark