The typical missile is not powerful enough to go to space. The typical missile is used as a short-distance weapon, usually less than 20 miles. Think "Air-to-Air" missile under the wing of a fighter jet.
There ARE missiles, called ICBMs (Inter-Continental Ballistic Missiles) that are specifically designed to launch payloads (explosives) from one country to another, but are NOT powerful enough to send anything into space.
The Redstone ICBM was the rocket selected for the first manned space flights, the MERCURY Missions. But this was NOT a "standard" Redstone missile; it needed MANY modifications, including a more powerful engine using a more powerful fuel, to put a man into space. for later flights, the ATLAS ICBM was used. The Titan II ICBM, again needing upgraded, was used for the Gemini Missions.
The Saturn V rocket used for Apollo was specifically designed for manned space launches. The Saturn vehicles were never intended as ICBM's.
Technically, NO, a missile CAN NOT launch anything int space. The standard "missile" does not have the power to put anything into space. Any missiles used for space shots must be modified, even completely rebuilt, to work as space launch vehicles. So, the desired "plan of attack" is to design the rocket SPECIFICALLY for space mission, and we no longer use converted or modified missiles.
The United States DOES NOT have any ground-launched missiles capable of shooting down satellites, nor do we have any air-launched missiles with that capability. It is RUMORED that some defense satellites carry their own missiles, but using them would be an act of war.
As well, adding defensive rockets to any satellite would add additional launch weight, which translates to a larger rocket, more fuels, and MUCH MUCH HIGHER costs to launch. Defensive missiles in satellites does NOT make any economic sense, even in war time. It is doubtful that any space craft in orbit today has any kind of offensive or defensive weapons.