Weird question, but I was wondering if when a person has a cancer tumor, a small portion was analyzed for DNA would the cancer cell have:
1.that person’s DNA
2.that person’s DNA but warped and mutated
3.or be a totally foreign substance
#2, although just “mutated,” no warpies here.
It depends how you define mutated 
DNA replication is not exact at the best of times, so some of your cells contain DNA that is not quite the same as the DNA you were conceived with. Most of the time, this is fine, and the cells work as well as you would expect. Sometimes, however, the tangles, replications, insertions, deletions and breaks leads cells to replicate uncontrollably, or to modify function. This could cause a tumour where the DNA is subtly (or wildly) different from the parent cell.
Epigenetic factors may have a role in tumour formation, too. This is where a chemical change from environmental factors in the DNA (usually methylation) causes a change in the expression of a gene (activation, deactivation, enhancement or suppression are all possibilities). This can change the cell into a cancerous one, whose DNA will be basically the same as the parent DNA.
Some viral infections can cause cancers, either by erroneous inclusion (where a fragment of the viral DNA gets incorporated into the cell DNA) or by epigenetic changes caused by the viral DNA presence. These tumours will have DNA that exhibits sequences of the virus mixed in with the parent DNA.
Finally, there are a class of transmissible tumours (like the Tasmanian Devil Facial Tumours). These are longliving cells with their own DNA that can grow and replicate wherever they find themselves. They have their own DNA completely independent of the host. However, there are no human transmissible cancers as far as I can see.
Si
You also tend to get a lot of aneuploidy in many tumors - extra or missing chromosomes.