This is a small tutorial showing how is done.

1. Get mp4box
2. Get the track ID of the subtitle(s)
Code:
mp4box -info sample.mp4
* Movie Info *
        Timescale 1000 - 4 tracks
        Computed Duration 00:02:55.427 - Indicated Duration 00:02:55.427
        Fragmented File: no
        File suitable for progressive download (moov before mdat)
        File Brand isom - version 512
                Compatible brands: isom iso2 avc1 mp41
        Created: UNKNOWN DATE   Modified: UNKNOWN DATE
File has root IOD (9 bytes)
Scene PL 0xff - Graphics PL 0xff - OD PL 0xff
Visual PL: ISO Reserved Profile (0x15)
Audio PL: AAC Profile @ Level 2 (0x29)
No streams included in root OD

iTunes Info:
        Name: If I Can't Have You
        Artist: Yvonne Elliman
        Album: Solo Night
        Writer: Barry, Robin and Maurice Gibb
        Album Artist: Yvonne Elliman
        Genre: Disco, Pop
        Created: 1978
        Encoder Software: Lavf58.17.101
1 UDTA types: meta (1)

Track # 1 Info - TrackID 1 - TimeScale 5000000
Media Duration 00:02:55.374 - Indicated Duration 00:02:55.374
Track has 1 edit lists: track duration is 00:02:55.375
Media Info: Language "Undetermined (und)" - Type "vide:avc1" - 5256 samples
Visual Track layout: x=0 y=0 width=960 height=720
MPEG-4 Config: Visual Stream - ObjectTypeIndication 0x21
AVC/H264 Video - Visual Size 960 x 720
        AVC Info: 1 SPS - 1 PPS - Profile High @ Level 3.1
        NAL Unit length bits: 32
        Pixel Aspect Ratio 1:1 - Indicated track size 960 x 720
        Chroma format YUV 4:2:0 - Luma bit depth 8 - chroma bit depth 8
        SPS#1 hash: EF179CBACC7085F90F1CA38E633ED0C376173C64
        PPS#1 hash: 57B6A76E3C7BFCCAEFC8060C61076BBA234904B3
Self-synchronized
        RFC6381 Codec Parameters: avc1.64001F
        Average GOP length: 47 samples

Track # 2 Info - TrackID 2 - TimeScale 44100
Media Duration 00:02:55.426 - Indicated Duration 00:02:55.426
Track has 1 edit lists: track duration is 00:02:55.427
Media Info: Language "English (eng)" - Type "soun:mp4a" - 7555 samples
MPEG-4 Config: Audio Stream - ObjectTypeIndication 0x40
MPEG-4 Audio AAC LC - 2 Channel(s) - SampleRate 44100
Synchronized on stream 1
        RFC6381 Codec Parameters: mp4a.40.2
Alternate Group ID 1
        All samples are sync

Track # 3 Info - TrackID 3 - TimeScale 1000
Media Duration 00:02:53.250 - Indicated Duration 00:02:53.250
Media Info: Language "Portuguese (por)" - Type "text:tx3g" - 77 samples
Unknown Text Stream
 Size 960 x 720 - Translation X=0 Y=0 - Layer 0
        RFC6381 Codec Parameters: tx3g
        All samples are sync

Track # 4 Info - TrackID 4 - TimeScale 1000
Media Duration 00:02:53.250 - Indicated Duration 00:02:53.250
Media Info: Language "English (eng)" - Type "text:tx3g" - 77 samples
Unknown Text Stream
 Size 960 x 720 - Translation X=0 Y=0 - Layer 0
        RFC6381 Codec Parameters: tx3g
        All samples are sync
3. Track ID 3 and 4 are the subtitles, remove with:
Code:
mp4box -rem 3 sample.mp4
Removing track ID 3
Saving sample.mp4: 0.500 secs Interleaving

mp4box -rem 4 sample.mp4
Removing track ID 4
Saving sample.mp4: 0.500 secs Interleaving
4. Done.