Yes, it could be built; but the cost/SqrFt of usable space would be prohibitive. Maybe if it's a hollow-core design it might make sence.

this new building is planned for Jeddah city saudi arabia on the red sea by Prince Al waleed ben Talal the known saudi investor

and it is called the MILE's tower (referring to its length)

Mega-tall buildings have more challenges than just staying up. There's people. What kind of elevator ride does it take to go up a MILE? How many staged elevators will it take? (That's a commute just to get in and out.) How about getting DOWN from a mile up in an emergency? How can you evacuate something that size? (Fire, earthquake, terrorist target (it did say Middle East)?) How about getting running water up that high? Fresh air into something that size? Heating, cooling, sunlight? It's going to make tremendous demands on environmental resources, and it's going to take a staggering amount of material (steel, cement, etc) to build it.

this building is acturly called Al Burj and it is supposed to be 1.2 km tall and it isn wicked and amazing.

Actually this building is'nt called AL Burj, the Al Burj is planned to be taller than the Burj Dubai and was originally intended to be built on the main trunk of the Palm Jumeriah but has been moved again and again due to it's weight. I have only seen two pictures of this proposed 'Mile Tower' one looks like a termite mound but is called "the ultima, 2milehigh" building, and a single tower with two flying buttresses. It is not even listed on the Kingdom Holding website-the company who is comissioning the tower.

in answer to bchiver's query, i have done some research on the Burj Dubai. The tower has 3 dedicated emergency lifts which automatically come into action when there is an emergency. They are seperate from the controls of the normal elevators, however they do run themselves which may result in accidents. Also the tower contains 9 fireproof rooms. 3 of these rooms are on the same floor at 3 different levels throughout the tower. They can withstand a burning fire outside for up to 2 hours and have a fresh air supply pumped into them through a flame retardant pipe. Also, like in the twin towers scenario, people could not escape down stairwells because they were burning, however in this tower, there are high powered fans, on every stair, that blast icy, fresh air into the stairs, pushing down the fire and sucking the smoke away, leaving the stairs clear. I think that this is a pretty good idea, but what would happen if a plane crashed into it??? I mean the building, lower down, in large and wide enough to hold 4 jumbo jets, so it may not cause to much damage, but further up near the spire it could probably sever the top off. CATASTROPHY!!!!!!!!!!!!!!!!!!!!!!!!

Also the elevators travel at 30m/s meaning it only takes 4minutes to reach the top. All of the 30 elevators are double deckers meaning a whole double elevator carriage can carry around 70people. The proposed Mile Tower, would take 9minutes to reach the top, so i hope that they will make some amenities in the lift like seats et cetera as i do not fancy sitting in a small box for 10minutes.