A motorized road ice scraper can remove about half an inch of ice at every passage. So you place the scraping heads of several of them on a beam, yet others on another beam etc., until you build a spoked wheel. You've now got a boring head - basically a vertical tunnel boring machine. Between head and head, nozzles can be set up to spray tiny jets of hot water under high pressure, to break down the ice and make the work easier for the scrapers. The water can be recycled indefinitely.
With sixteen orders of scrapers and turning at ten RPM, which isn't much when boring through ice, the disk can bore at about two meters per minute assuming each head has the same efficiency of a road scraper. The pulverized ice can be pumped up using tubes filled with gas (I expect that occasionally the tube will need to be flushed with hot gas to prevent blockages). Or it can be pressed into hollow, Teflon-coated tubes using pistons.
The scraping disk is lowered from the surface, with the submarine on top of it. When it arrives at the ocean, it is lowered further so that the submarine is released gently, then it is brought up again.
Depending on the ice resistance and risk of a collapse, the tunnel might be excavated by a two-part boring head: the boring disk itself, over which the sub is hosted. And a hollow vertical cylinder, as wide as the tunnel, with vertical treads, capable of going up and down. Instead of the winches being on the surface, and ten kilometers' worth of cables be paid out, this cylinder would lower itself inside the tunnel and keep the boring disk going down at constant speed. It could have horizontal drills capable of penetrating for several tens of meters inside the walls, injecting water just above 0 °C and letting it freeze in place (allowing for ice expansion, of course - we don't want to frack the tunnel walls). Or it could keep a central layer at a temperature just above 0 °C. In both cases, the end result is that any cracks or vacuum pockets or irregularities in the tunnel walls get replaced by solid ice.
At one seventh G, the risk of the tunnel walls becoming so much denser than the average Europan ice, that they get torn down by their own weight should be negligible even when considering ten kilometers' worth of depth. Also, a height of ten kilometers (1350 m Earth equivalent) are well within the compressive strength of Ice XI.
(the melting method to reach the ocean of Europa is detailed in Charles Sheffield's Cold as Ice, using a fusion generator devised by Cyrus Mobarak).
Following up to Richard Hansen's comment, I found out that this design has already been developed and tested. The speed of the Rapid Access Ice Drill is around 3300 meters in 200 hours, including setting up camp and dismantling everything; I think it's safe to assume around 25 meters an hour. The RAID uses slowly rotating medium speed drills, electrically powered; using fusion power sources is likely to go a lot faster, e.g. combining hot water drilling and grinding heads.
Orbital microwave cannon - it would melt the ice, then boil the water, and finally disperse the water vapour. This has the advantage of very low risk from cave-ins (but still requires lowering the sub somehow). On the other hand, a ten-kilometer borehole full of microwaved gas without a real atmosphere, in about one seventh gee, will create a plume possibly high enough to interfere with orbital vehicles before being dispersed by the solar wind. Internal refraction of microwaves and ablation from the rising vapor plume will also cause the tunnel to grow larger at the mouth, and require proportionally more energy to be excavated.
Orbital kinetic strike - assuming a very dense impactor (depleted uranium/tungsten alloy), the Newton penetration formula in ice XI gives a length factor of around 20: that is, the penetrator will punch 20 times its length before dispersing its momentum. Drilling a ten-kilometer bore will require a 500m solid metal penetrator, or multiple accurate KEW strikes. There is the risk of the ice fracturing, which can interfere with the sub operations.