You can look up the ancestors and children in the various Gene Ontology browsers such as AmiGo or QuickGo e.g. http://www.ebi.ac.uk/QuickGO/GTerm?id=GO:0046222#term=ancchart
There are also various ways to process the data programmatically using perl/java
I don't think you can find GO terms which are associated with cancer because you could pretty much associate almost any GO term with having some relation to cancer. There are no specific cancer GO terms. All are related to some normal cell function that you could argue are dysregulated in cancer like angiogenesis, cell cycle checkpoint or kinase activity to name a few.
I think your best bet is to search for cancer associated genes here (COSMIC database) : http://cancer.sanger.ac.uk/cancergenome/projects/census/
...and then filter your gene list based on this database.
In addition to the comments of Mr Bucxkowicz, you can also introduce your list in the DAVID db, to analyze the possible relation (and enrichment) of your gene list in particular pathways, genetic associated diseases (included cancer associations) and other interesting stuffs.
Basically i want to make a subset of biological processes from a big list of GO terms.
I could do that manually but i feel that this manual annotation is limited by my knowledge about cancer. For example, i know that apoptosis, angiogenesis or inflammation are related with cancer but some processes could be out of my knowledge.