MongoDB GridFS delete operation too slow while mongod process takes up 100% CPU

I'm using Python (CPython 2.7.3 on Debian 7.8 amd64) with pymongo driver (version 2.7.2) to connect to a MongoDB (db version v2.4.12) database which has solely been used to store files in a GridFS storage collection. While mongodb can find the _id of a file object with a given filename instantaneously, requesting to delete that file given its _id takes an unusual 10s of seconds to complete during which mongod takes up 100% CPU time.

I'm not a mongodb expert and have not done any performance optimizations on it, but still I think there is something wrong here. What am I missing and how can I pinpoint and solve this problem?

I should add that there are millions of files in this collection with nearly 700GB size, and the free space left on disk is running very low.

Edit:

> db.stats()
{
        "db" : "imagedb",
        "collections" : 6,
        "objects" : 80435832,
        "avgObjSize" : 6521.6805692766375,
        "dataSize" : 524576802628,
        "storageSize" : 563036266512,
        "numExtents" : 308,
        "indexes" : 7,
        "indexSize" : 6604172176,
        "fileSize" : 588057149440,
        "nsSizeMB" : 16,
        "dataFileVersion" : {
                "major" : 4,
                "minor" : 5
        },
        "ok" : 1
}