Disclaimer: This is a partial answer, as I don't have access to any of the sources I'm summarizing summarizations of. Feel free to edit or change to community wiki. Most of the summaries used are made by wikipedia user Paul H, who is by the looks an experienced geologist and woo fighter (Just look at the talk page for Pumapunku). I've no reason to doubt the correctness of the sources he cites nor his summary of them.
No, Pumapunku was not built by aliens.
Pumapunku is the site of a large temple complex dating from around 500 AD. Many objects have been identified pointing to human construction, including stone tools. There is abundant evidence that this site was part of the thriving Tiwanaku civilization.
The blocks were too big to be moved
False. The largest block on the site weighed around 130 tons, and was determined to have been mined 10km away from the site. There are multiple means by which the builders may have moved these blocks, including ramps, sleds and ropes made of llama skin. The precise means by which these blocks were positioned is unknown, mostly because the Tiwanaku civilization did not have a written record. There were many civilizations that independently developed the tools and techniques required to build megalithic stone structures. The Tiwanaku were an advanced civilization and were adept at stone and metalwork, being able to cold forge metals and produce alloys.
Advanced tools were used
Advanced tools likely were used - this was an advanced civilization. There's little reason to doubt that they were able to craft hardened metals for drilling, gouging and hammering stone.
These tools could not have been "stone age" tools
The Tiwanaku were not a stone age civilization. They were adept metalworkers. However, many of the tools used could have been "stone age" tools, where metallic tools were not required. Rock hammers were found on site, for example. Looting of the sites over the years has meant that many or all of the original tools used were likely removed from the site.
The blocks are a mix of granite and diorite, and diorite is so hard that diamond-tipped tools would be required.
False. Not only is diorite not that hard, but Pumapunku is comprised of andesite and sandstone.
References:
If anybody can help track these down so we can source some quotes and confirm the answers, it would be very helpful.
Vranich, A., 2006, The Construction and Reconstruction of Ritual Space at Tiwanaku, Bolivia: A.D. 500-1000. Journal of Field Archaeology 31(2)
Protzen, J.-P., and S.E.. Nair, 2000, On Reconstructing Tiwanaku Architecture: The Journal of the Society of Architectural Historians. vol. 59, no. 3
Protzen, Jean-Pierre; Stella Nair, 1997, Who Taught the Inca Stonemasons Their Skills? A Comparison of Tiahuanaco and Inca Cut-Stone Masonry: The Journal of the Society of Architectural Historians. vol. 56, no. 2
Kolata, A. L., 1993, The Tiwanaku: Portrait of an Andean Civilization. Blackwell Publishers, Cambridge, United Kingdom
Kolata, Alan L., 2003, Tiwanaku and Its Hinterland: Archaeology and Paleoecology of an Andean Civilization, Vol. 2. Smithsonian Institution Press, Washington, DC.
Ponce Sanginés, C. and G. M. Terrazas, 1970, Acerca De La Procedencia Del Material Lítico De Los Monumentos De Tiwanaku. Publication no. 21. Academia Nacional de Ciencias de Bolivia
Protzen, Jean-Pierre; Stella Nair, 1997, Who Taught the Inca Stonemasons Their Skills? A Comparison of Tiahuanaco and Inca Cut-Stone Masonry: The Journal of the Society of Architectural Historians. vol. 56, no. 2 is available at http://michaelsheiser.com/PaleoBabble/2009/07/stone-masonry-and-engineering-at-machu-picchu-no-aliens-needed/
